The generator matrix

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

generates a code of length 32 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 26.

Homogenous weight enumerator: w(x)=1x^0+36x^26+86x^27+166x^28+198x^29+197x^30+254x^31+260x^32+234x^33+193x^34+150x^35+93x^36+74x^37+47x^38+18x^39+23x^40+6x^41+7x^42+4x^43+1x^44

The gray image is a code over GF(2) with n=128, k=11 and d=52.
This code was found by Heurico 1.16 in 0.128 seconds.