The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  0  1  2  X  1  1  1  2  1  1  1  2  1  X  1  1  2  1  1  1  1  1  0
 0  X  0  0  0  0  0  2  2  X X+2  X  X  X X+2  X  0 X+2  2  X  2  2  X  0 X+2 X+2 X+2  2  2  2  0  0  X X+2 X+2  2 X+2  X  X  X  X  0  0  0
 0  0  X  0  0  2 X+2  X  X  X  X  X X+2  0  0  0  2  2 X+2  X  2  X  0  X  X  0  2  X  X  2  0  X  X  0  0  2 X+2 X+2  2 X+2  0 X+2 X+2  0
 0  0  0  X  0 X+2 X+2  X  2 X+2 X+2  0  0  X  X  2  X  2 X+2  0 X+2  0  0 X+2  2  X  X  0  0  2  2 X+2  2  2 X+2  0 X+2  0  X  X  0  X  2  0
 0  0  0  0  X  X  2 X+2  X X+2  2  2  X  2 X+2  X  X  2  2 X+2  0  0 X+2  2  X  X  2  2  X  2 X+2  X  2 X+2  X  2 X+2  0  2  X  2  X  0  X

generates a code of length 44 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 38.

Homogenous weight enumerator: w(x)=1x^0+124x^38+245x^40+456x^42+520x^44+354x^46+173x^48+102x^50+48x^52+18x^54+4x^56+2x^58+1x^72

The gray image is a code over GF(2) with n=176, k=11 and d=76.
This code was found by Heurico 1.16 in 0.217 seconds.