The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 1 X 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1
0 2X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2X 0 0 2X 2X 0 2X 0 2X 0 2X 2X 0 2X 0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 0 2X 2X 2X 0 2X 0 2X 2X 2X 2X 2X 0 0 2X 0 2X 2X 0 2X 2X 2X 0 0 0 2X 0 0 0 0 2X 0 0 2X 2X 0 0
0 0 2X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2X 0 2X 2X 0 0 2X 0 2X 0 2X 2X 0 2X 2X 2X 0 2X 2X 2X 2X 2X 2X 0 2X 2X 2X 0 2X 2X 2X 0 2X 0 2X 2X 2X 2X 2X 2X 0 2X 0 0 2X 2X 2X 0 0 0 0 2X 0 0 2X 2X 0 2X 0 2X 0 2X 0
0 0 0 2X 0 0 0 0 0 0 0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 0 2X 0 2X 2X 2X 2X 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2X 2X 2X 2X 2X 2X 0 0 2X 2X 2X 2X 2X 2X 0 0 2X 2X 0 2X 2X 0 0 0 0 0 2X 2X 2X 2X 0 0 2X 2X 0 0 0
0 0 0 0 2X 0 0 0 2X 2X 2X 2X 2X 0 2X 2X 0 0 0 0 0 0 0 0 0 0 0 0 0 2X 2X 2X 2X 2X 2X 0 2X 0 2X 0 2X 2X 0 2X 2X 2X 2X 0 2X 2X 2X 0 2X 0 2X 0 2X 2X 2X 2X 2X 2X 0 2X 0 0 0 0 2X 0 2X 2X 0 2X 2X 2X 0 2X 0 2X 0
0 0 0 0 0 2X 0 2X 2X 2X 0 0 0 0 2X 2X 2X 2X 0 0 0 0 0 0 2X 2X 2X 2X 2X 2X 0 0 2X 0 0 0 2X 0 2X 2X 0 2X 2X 0 2X 0 0 2X 0 2X 2X 2X 0 2X 2X 0 2X 0 2X 2X 2X 0 2X 2X 0 2X 0 2X 2X 2X 0 2X 0 2X 0 2X 2X 2X 2X 2X 0
0 0 0 0 0 0 2X 2X 0 2X 2X 0 2X 2X 2X 0 0 2X 0 0 2X 2X 2X 2X 2X 2X 0 0 0 0 2X 0 2X 2X 0 0 0 2X 2X 2X 2X 2X 0 0 0 2X 0 2X 2X 2X 2X 2X 2X 0 2X 2X 2X 0 0 0 0 0 2X 0 0 0 0 2X 0 2X 0 0 0 2X 0 0 0 0 2X 2X 0
generates a code of length 81 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 76.
Homogenous weight enumerator: w(x)=1x^0+28x^76+17x^78+32x^79+21x^80+832x^81+20x^82+32x^83+12x^84+22x^86+2x^88+4x^90+1x^158
The gray image is a code over GF(2) with n=648, k=10 and d=304.
This code was found by Heurico 1.16 in 0.407 seconds.