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 X 1 1 1 1 1 1 1 X 1 1 1 1 1 1 X X X 1 1 X X X 1 1
0 2X 0 0 0 0 0 0 0 0 2X 2X 0 0 0 2X 0 0 0 0 2X 2X 2X 2X 0 2X 2X 2X 0 2X 2X 0 0 2X 0 2X 2X 2X 2X 2X 2X 2X 0 0 2X 0 2X 0 0 0 2X 0
0 0 2X 0 0 0 0 0 0 2X 2X 2X 0 2X 2X 0 0 0 2X 2X 2X 2X 2X 2X 0 2X 0 0 2X 2X 0 2X 2X 2X 2X 2X 2X 0 0 2X 2X 0 2X 0 0 0 0 2X 0 0 2X 0
0 0 0 2X 0 0 0 0 0 2X 0 2X 2X 2X 0 2X 0 2X 2X 0 0 0 0 0 2X 0 2X 2X 0 2X 2X 0 0 2X 0 2X 0 2X 0 0 2X 0 2X 2X 2X 2X 2X 0 0 2X 2X 0
0 0 0 0 2X 0 0 0 2X 0 0 2X 2X 0 2X 2X 0 0 2X 2X 0 0 0 2X 2X 2X 2X 0 0 0 2X 0 2X 0 0 0 2X 2X 2X 0 2X 2X 0 2X 0 0 2X 2X 2X 2X 0 0
0 0 0 0 0 2X 0 0 2X 0 2X 0 0 2X 2X 2X 0 2X 2X 0 0 0 0 2X 2X 0 0 2X 2X 2X 0 2X 2X 2X 2X 0 0 0 0 2X 0 0 2X 2X 0 2X 2X 0 2X 0 0 2X
0 0 0 0 0 0 2X 0 2X 2X 2X 0 0 0 2X 2X 2X 0 0 2X 0 0 2X 0 2X 0 2X 2X 0 0 2X 0 0 0 2X 2X 0 0 0 2X 2X 2X 2X 2X 0 2X 0 2X 0 2X 2X 0
0 0 0 0 0 0 0 2X 2X 2X 0 0 2X 2X 2X 0 2X 0 2X 0 0 2X 2X 0 0 0 2X 2X 2X 0 0 0 2X 2X 0 0 2X 2X 0 2X 2X 2X 2X 2X 0 0 0 0 0 0 0 0
generates a code of length 52 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 44.
Homogenous weight enumerator: w(x)=1x^0+41x^44+10x^46+107x^48+50x^50+1652x^52+62x^54+71x^56+6x^58+23x^60+20x^64+4x^68+1x^88
The gray image is a code over GF(2) with n=416, k=11 and d=176.
This code was found by Heurico 1.16 in 0.172 seconds.