The generator matrix

 1  1  1  1  1  1  1  1  1  1  X  1  X  1  0  1  0  0  1  X  0 X^2  0  1  1  0  1 X^2  X  1  1  1
 0  X  0  0  0  X X^2+X  X  0 X^2 X^2  X  X X^2+X  X X^2  X  0 X^2  X  0  X  0 X^2 X^2  X  0  0 X^2 X^2  X  0
 0  0  X  0  X  X X^2+X  0  0  0 X^2+X  X  0  X  0  X  X  X  X X^2+X X^2  0 X^2  0 X^2+X X^2  0  X  X X^2+X X^2+X  0
 0  0  0  X  X  0 X^2+X  X  0  X  X X^2 X^2+X X^2+X  0 X^2  X X^2 X^2 X^2  X X^2+X  X X^2  X  0  X  X X^2 X^2+X X^2  0
 0  0  0  0 X^2  0  0  0  0  0  0  0 X^2 X^2  0 X^2 X^2 X^2  0 X^2  0  0 X^2  0 X^2  0 X^2  0 X^2  0  0  0
 0  0  0  0  0 X^2  0  0  0  0  0  0 X^2 X^2 X^2 X^2  0  0 X^2  0  0 X^2  0  0 X^2 X^2 X^2  0  0 X^2  0  0
 0  0  0  0  0  0 X^2  0  0  0 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2
 0  0  0  0  0  0  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2  0  0  0  0 X^2 X^2 X^2  0 X^2
 0  0  0  0  0  0  0  0 X^2 X^2 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2  0 X^2 X^2 X^2 X^2 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 22.

Homogenous weight enumerator: w(x)=1x^0+27x^22+60x^23+151x^24+246x^25+379x^26+484x^27+918x^28+1216x^29+1596x^30+2076x^31+2004x^32+2072x^33+1690x^34+1276x^35+896x^36+508x^37+359x^38+184x^39+113x^40+50x^41+43x^42+16x^43+10x^44+4x^45+2x^46+3x^48

The gray image is a linear code over GF(2) with n=128, k=14 and d=44.
This code was found by Heurico 1.16 in 6.63 seconds.