The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  0  1  1  1  1  0  1  1  0  1
 0  X  0  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2+X  X  X  X X^2+X X^2+X  X  X  X X^2  X  X
 0  0  X  0  0  0  0  0  0  0  X X^2+X  X X^2+X X^2+X  X X^2+X  0 X^2 X^2 X^2  0 X^2+X X^2  X  X  X X^2+X X^2 X^2+X  X  X
 0  0  0  X  0  0  0  X X^2+X  X  X  X  0 X^2+X  0 X^2+X X^2  X  0 X^2  X X^2+X X^2 X^2  0 X^2+X X^2+X X^2+X  X  0  0 X^2+X
 0  0  0  0  X  0  X  X  X X^2  0  0 X^2 X^2+X  X X^2+X  X  X X^2+X  X  0 X^2  X  0  X X^2 X^2 X^2+X  X  0  0  X
 0  0  0  0  0  X  X X^2 X^2+X X^2+X  0  X  X  X  0 X^2  X  0 X^2+X  0  X X^2  0 X^2+X X^2  0 X^2+X  X  0  0  X X^2
 0  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 X^2  0  0 X^2  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+293x^24+690x^26+1029x^28+256x^29+2172x^30+1792x^31+3830x^32+1792x^33+2292x^34+256x^35+1108x^36+604x^38+194x^40+66x^42+7x^44+1x^48+1x^56

The gray image is a linear code over GF(2) with n=128, k=14 and d=48.
This code was found by Heurico 1.16 in 40.1 seconds.