The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2  1  X  1 X^2+X  1  1  X  1  1  1  1  0  1  1  0  1  1  1  1  0  1  1  X
 0  1  1 X^2+X X^2+X+1  1  0 X+1  1  X  1 X^2+1  1  0 X^2  1  1 X^2+X+1 X^2+X+1 X^2+X  1 X+1 X^2+X  1 X^2 X+1 X^2+X+1 X^2+X  X X^2+X+1 X^2+X+1 X^2+X
 0  0  X  0 X^2+X  0 X^2+X X^2 X^2+X X^2+X  X X^2 X^2  0  X X^2+X X^2+X X^2+X X^2+X X^2  0 X^2  0 X^2  X X^2  0 X^2 X^2+X X^2 X^2  X
 0  0  0 X^2  0  0  0 X^2  0  0 X^2  0 X^2 X^2 X^2  0  0  0 X^2 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  0 X^2  0  0  0 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0  0 X^2  0  0 X^2 X^2  0  0 X^2 X^2
 0  0  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0
 0  0  0  0  0  0 X^2  0  0 X^2  0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  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+107x^26+96x^27+270x^28+352x^29+423x^30+560x^31+467x^32+608x^33+456x^34+352x^35+188x^36+64x^37+96x^38+16x^39+28x^40+5x^42+6x^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 0.404 seconds.