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

generates a code of length 32 over Z2[X]/(X^3) 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 linear code over GF(2) with n=128, k=11 and d=52.
This code was found by Heurico 1.16 in 0.127 seconds.