The generator matrix

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

generates a code of length 32 over Z2[X]/(X^3) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+47x^20+70x^22+32x^23+186x^24+136x^25+255x^26+680x^27+429x^28+1952x^29+620x^30+3328x^31+825x^32+3376x^33+677x^34+1936x^35+457x^36+672x^37+310x^38+160x^39+74x^40+8x^41+89x^42+8x^43+27x^44+24x^46+2x^48+3x^50

The gray image is a linear code over GF(2) with n=128, k=14 and d=40.
This code was found by Heurico 1.16 in 5.63 seconds.