The generator matrix

 1  0  1  1  1  0  1  1  X  1 X^2+X  1  1  1  0  1  1  1 X^2+X  X  1 X^2  1  1  1  1  1 X^2  1  1  1  1
 0  1  1  0 X+1  1  X X^2+X+1  1 X^2+1  1 X^2+X X^2 X^2+X+1  1 X+1  0  X  1  1 X^2+1  1 X^2+X  1  1  X X^2+X+1  1 X+1 X^2+X+1 X+1  0
 0  0  X X^2+X  0 X^2+X  X X^2+X  X  0 X^2  0  X X^2+X X^2  0  0  X X^2  X X^2  X  0 X^2+X X^2+X X^2+X  X X^2+X  0 X^2+X  X  0
 0  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0  0 X^2  0  0 X^2  0 X^2 X^2  0
 0  0  0  0 X^2  0  0  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0 X^2 X^2 X^2  0  0  0 X^2 X^2  0  0
 0  0  0  0  0 X^2  0  0 X^2  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2  0
 0  0  0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2 X^2  0  0  0  0  0 X^2 X^2 X^2  0
 0  0  0  0  0  0  0 X^2 X^2  0  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0  0 X^2 X^2 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+49x^24+44x^25+122x^26+268x^27+389x^28+664x^29+893x^30+1084x^31+1209x^32+1072x^33+888x^34+644x^35+374x^36+264x^37+118x^38+52x^39+21x^40+4x^41+22x^42+5x^44+5x^46

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 1.34 seconds.