The generator matrix

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

generates a code of length 32 over Z2[X]/(X^3) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+123x^24+8x^25+360x^26+88x^27+641x^28+328x^29+1150x^30+600x^31+1535x^32+600x^33+1268x^34+328x^35+662x^36+88x^37+256x^38+8x^39+99x^40+36x^42+9x^44+2x^46+2x^48

The gray image is a linear code over GF(2) with n=128, k=13 and d=48.
This code was found by Heurico 1.16 in 1.92 seconds.