The generator matrix

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

generates a code of length 32 over Z2[X]/(X^3) who´s minimum homogenous weight is 25.

Homogenous weight enumerator: w(x)=1x^0+56x^25+141x^26+140x^27+192x^28+306x^29+438x^30+526x^31+547x^32+526x^33+394x^34+306x^35+196x^36+126x^37+104x^38+50x^39+20x^40+10x^41+9x^42+2x^43+4x^44+2x^46

The gray image is a linear code over GF(2) with n=128, k=12 and d=50.
This code was found by Heurico 1.16 in 8.83 seconds.