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 X 1 1 X 1 1 X 1 1 1 1 X 1 1 X X X 1 1 X X 2 0 X X 1 1 2 0 X X X 1 2 0 2 X X 2 X 1 2 0 2 X X 2 X 2 0 X 2 X 1
0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 0 2 2 0 2 2 0 2 2 0 2 0 2 2 0 2 0 2 0 0 2 2 0 2 2 0 2 0 2 2 2 0 2 0 0 2 2 0 0 2 0 0 2 2 2 0 2 0 0 0 2 2 2 0 0 0
generates a code of length 80 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 84.
Homogenous weight enumerator: w(x)=1x^0+1x^84+10x^85+2x^86+2x^87
The gray image is a code over GF(2) with n=320, k=4 and d=168.
This code was found by Heurico 1.16 in 0.251 seconds.