The generator matrix

 1  0  0  1  1  1 X^2+X  1  1  1  X X^2+X  1  0  X  1  X  1  1  1  1 X^2  1  0  0  1 X^2+X  X  1  1  1  1
 0  1  0  1  0  1  1  X  1  X  1  1 X+1  X  1  0 X^2+X X^2+X X^2+1  0 X^2+X+1  1 X^2+X  1 X^2+X  1  1  X  1 X^2+1  0  0
 0  0  1  1  1  0  1 X+1  1  X X^2+X X^2+1  X  1  0 X+1  1 X^2  1 X^2+X  X  1  1  0  1 X^2  X  1 X^2+X+1 X^2 X^2+X+1  X
 0  0  0  X  0  0  0  0  0  0  0 X^2 X^2  X  X X^2+X X^2+X  X X^2+X  X  X  X  X  X  X X^2  0  X X^2  0  X  X
 0  0  0  0  X  0  0  0 X^2  X  X X^2+X X^2+X X^2+X X^2+X X^2+X X^2 X^2 X^2+X X^2+X  X  0 X^2  0  0 X^2+X  0 X^2  0  X X^2+X X^2
 0  0  0  0  0  X X^2+X X^2+X  0  X X^2+X  0 X^2 X^2+X  X  0 X^2  0  X  X X^2 X^2+X  X  0 X^2  X  X X^2+X  0  X X^2+X 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+64x^24+216x^25+684x^26+860x^27+1845x^28+2260x^29+3925x^30+3762x^31+5318x^32+3964x^33+4063x^34+2242x^35+1869x^36+828x^37+534x^38+166x^39+117x^40+28x^41+9x^42+10x^43+2x^44+1x^54

The gray image is a linear code over GF(2) with n=128, k=15 and d=48.
This code was found by Heurico 1.16 in 16.6 seconds.