The generator matrix

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

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+27x^26+144x^28+201x^30+292x^32+194x^34+132x^36+22x^38+2x^40+3x^42+4x^44+1x^46+1x^48

The gray image is a linear code over GF(2) with n=128, k=10 and d=52.
This code was found by Heurico 1.16 in 0.0454 seconds.