The generator matrix

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

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+106x^22+128x^23+378x^24+420x^25+628x^26+732x^27+947x^28+1180x^29+1235x^30+1610x^31+1461x^32+1616x^33+1407x^34+1272x^35+1028x^36+768x^37+594x^38+324x^39+256x^40+108x^41+116x^42+28x^43+25x^44+4x^45+9x^46+2x^47+1x^50

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 24.7 seconds.