The generator matrix

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

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+79x^24+450x^25+1253x^26+2062x^27+3721x^28+4692x^29+7189x^30+7994x^31+9959x^32+8408x^33+7882x^34+4790x^35+3592x^36+1852x^37+938x^38+382x^39+177x^40+86x^41+17x^42+4x^43+7x^44+1x^46

The gray image is a linear code over GF(2) with n=128, k=16 and d=48.
This code was found by Heurico 1.13 in 19.6 seconds.