The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 X^2 X^2  1  X  1  1  X  1
 0  X  0  0  0  0  0  0  0 X^2+X  X  X  X  0  X X^2+X X^2 X^2+X  0 X^2 X^2 X^2 X^2+X X^2  X  0  X X^2  0  X X^2 X^2
 0  0  X  0  0  0  X X^2+X  X X^2  X X^2+X  0 X^2+X  0 X^2+X X^2+X  X X^2  0 X^2 X^2+X X^2 X^2+X  0  X X^2 X^2  X X^2 X^2  0
 0  0  0  X  0  X  X  X  0 X^2+X X^2  X X^2+X  X X^2+X X^2 X^2  X X^2  X X^2 X^2+X X^2+X  0  0  X  0 X^2  0  X  0  X
 0  0  0  0  X  X  0  X X^2+X  X  0  X X^2 X^2+X X^2  0 X^2+X  0  X X^2  0 X^2+X X^2 X^2  X  0  X  X  X X^2+X X^2+X  0
 0  0  0  0  0 X^2  0  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0  0
 0  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0  0  0  0 X^2 X^2 X^2 X^2  0  0  0  0  0  0 X^2 X^2 X^2  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+112x^24+340x^26+618x^28+128x^29+1039x^30+896x^31+1922x^32+896x^33+1095x^34+128x^35+557x^36+325x^38+112x^40+17x^42+5x^44+1x^56

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 1.99 seconds.