The generator matrix

 1  0  1  1  1 X^2+X  1  1  0  1  1 X^2+X  1  1  0  1  1  0 X^2+X  1 X^2+X  1 X^2+X  1  1  1  0  1  0  1  X  1
 0  1 X+1 X^2+X  1  1  0 X+1  1 X^2+X X^2+1  1  0 X+1  1 X^2+X X^2+1  1  1 X+1  1 X^2+1  1  0 X^2+X X^2+1  1  0  1 X+1  0  0
 0  0 X^2  0  0  0  0  0  0  0  0  0 X^2  0  0 X^2 X^2  0  0  0 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0
 0  0  0 X^2  0  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 X^2  0  0 X^2
 0  0  0  0 X^2  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 X^2  0  0 X^2 X^2  0 X^2  0  0 X^2
 0  0  0  0  0 X^2  0  0  0  0  0 X^2  0 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0
 0  0  0  0  0  0 X^2  0  0  0  0 X^2  0  0 X^2 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2  0 X^2  0  0 X^2 X^2  0
 0  0  0  0  0  0  0 X^2  0  0 X^2  0  0  0 X^2  0 X^2 X^2 X^2  0 X^2  0 X^2  0 X^2 X^2 X^2  0  0 X^2  0 X^2
 0  0  0  0  0  0  0  0 X^2  0 X^2 X^2 X^2  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0 X^2  0  0  0 X^2  0 X^2  0
 0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2 X^2  0 X^2 X^2  0 X^2  0  0  0 X^2  0 X^2 X^2  0 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+38x^22+10x^23+101x^24+74x^25+206x^26+536x^27+428x^28+1944x^29+765x^30+3580x^31+988x^32+3580x^33+812x^34+1944x^35+440x^36+536x^37+197x^38+74x^39+75x^40+10x^41+22x^42+12x^44+7x^46+3x^48+1x^54

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 4.59 seconds.