The generator matrix

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

generates a code of length 32 over Z2[X]/(X^2) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+61x^20+62x^21+198x^22+232x^23+460x^24+722x^25+1032x^26+1420x^27+1963x^28+2488x^29+2871x^30+3328x^31+3239x^32+3124x^33+2834x^34+2536x^35+1923x^36+1534x^37+1105x^38+632x^39+488x^40+250x^41+132x^42+44x^43+53x^44+12x^45+17x^46+4x^48+2x^50+1x^54

The gray image is a linear code over GF(2) with n=64, k=15 and d=20.
This code was found by Heurico 1.16 in 36.1 seconds.