The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  X  0  1  1  X  1  0  1  1  1  X  1  1  0  X  1  1 X^2  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 X^2+X  X  0 X^2+X X^2+X  0  X  0  0 X^2 X^2+X X^2+X  X  X X^2+X X^2 X^2  0  0  0
 0  0 X^2  0  0  0  0  0 X^2  0  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0  0
 0  0  0 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0  0 X^2 X^2
 0  0  0  0 X^2  0  0  0  0  0 X^2  0 X^2  0 X^2  0 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2
 0  0  0  0  0 X^2  0  0  0 X^2 X^2 X^2  0 X^2  0  0  0 X^2 X^2  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0  0  0
 0  0  0  0  0  0 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2 X^2  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2  0  0  0
 0  0  0  0  0  0  0 X^2  0 X^2 X^2  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0  0  0  0  0  0  0  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+48x^24+36x^26+16x^27+208x^28+80x^29+274x^30+160x^31+419x^32+160x^33+274x^34+80x^35+174x^36+16x^37+54x^38+34x^40+2x^42+10x^44+2x^48

The gray image is a linear code over GF(2) with n=128, k=11 and d=48.
This code was found by Heurico 1.16 in 0.133 seconds.