The generator matrix

 1  0  0  0  0  0  0  1  1  1  1  X  1  1  X  1  X  X  1  1  X  1  X  1  X  X  0  X  X  1  1  1
 0  1  0  0  0  0  0  X  1  1 X+1  1 X+1  0  1  1  0  0  X  X  0  0  1  0  0  X  0  1  1 X+1  X  X
 0  0  1  0  0  0  0  0  0  0  0  0 X+1  1  1  X  1  X X+1  1  0  1  X  X  0  1  X  0 X+1 X+1 X+1  0
 0  0  0  1  0  0  0  0  0  0  0  0  0  X  1 X+1 X+1  X  1  X  1  1  0 X+1  X X+1  1 X+1 X+1  1 X+1  1
 0  0  0  0  1  0  0  1 X+1  X  X  1  0 X+1  1  X  0  X  0  X  1  0  1  1  1  1  0  0 X+1 X+1 X+1  1
 0  0  0  0  0  1  0  1  X X+1  0  1  X  X  0 X+1 X+1  1 X+1  1  X  X  X  X X+1 X+1  1  X  0 X+1 X+1  0
 0  0  0  0  0  0  1  1  0  X X+1 X+1  X  X  0  1  X  1  0  0  0  1 X+1  1  1  1  X  X  1  X  0  1

generates a code of length 32 over Z2[X]/(X^2) who´s minimum homogenous weight is 22.

Homogenous weight enumerator: w(x)=1x^0+85x^22+146x^23+274x^24+384x^25+603x^26+818x^27+943x^28+1034x^29+1400x^30+1660x^31+1577x^32+1632x^33+1366x^34+1356x^35+1062x^36+676x^37+541x^38+338x^39+218x^40+112x^41+95x^42+34x^43+19x^44+2x^45+6x^46+2x^48

The gray image is a linear code over GF(2) with n=64, k=14 and d=22.
This code was found by Heurico 1.16 in 23.2 seconds.