The generator matrix

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

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+40x^26+162x^27+279x^28+358x^29+462x^30+558x^31+508x^32+456x^33+467x^34+336x^35+221x^36+142x^37+49x^38+30x^39+11x^40+4x^41+5x^42+2x^43+4x^44+1x^46

The gray image is a linear code over GF(2) with n=128, k=12 and d=52.
This code was found by Heurico 1.16 in 0.274 seconds.