The generator matrix

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

generates a code of length 32 over Z2[X]/(X^3) who´s minimum homogenous weight is 23.

Homogenous weight enumerator: w(x)=1x^0+54x^23+158x^24+276x^25+431x^26+498x^27+889x^28+1216x^29+1576x^30+2016x^31+2000x^32+2048x^33+1703x^34+1312x^35+931x^36+496x^37+356x^38+202x^39+104x^40+60x^41+25x^42+14x^43+11x^44+4x^46+1x^48+1x^50+1x^52

The gray image is a linear code over GF(2) with n=128, k=14 and d=46.
This code was found by Heurico 1.16 in 6.98 seconds.