The generator matrix

 1  0  0  0  0  0  0  0  1  1  1  1  1  0  1  1  X  X  1  1  X  1  X  0  1  1  X  1  0  1  1  1
 0  1  0  0  0  0  0  0  0  X  0  X  0  X  0  1  1  1 X+1  X  1  0  1  1  1  X  0  X  1  X  0  0
 0  0  1  0  0  0  0  0  0  X  1  1  0  1  X  X  1  0  1  1  X X+1  X  X X+1  0  1  0 X+1  X  1  0
 0  0  0  1  0  0  0  0  1  0  0  1 X+1  1 X+1  X  X X+1  1 X+1  0 X+1 X+1  1  1 X+1 X+1  0  X  X  1  0
 0  0  0  0  1  0  0  0  1  0 X+1  0  1 X+1  X X+1  0  X  X  1  X  1  0 X+1  X X+1  0  0 X+1  X  1  0
 0  0  0  0  0  1  0  0  1  1  1  0  X X+1  1  X X+1  0  1  0  0 X+1  1  1 X+1  0 X+1 X+1 X+1 X+1  X  0
 0  0  0  0  0  0  1  0  1  1  X X+1 X+1  1  0  1  X X+1  0  0  1  1 X+1 X+1  1  1  0  1 X+1  X  0  0
 0  0  0  0  0  0  0  1  X  1 X+1  X  1 X+1  1  0 X+1 X+1  0  0 X+1  0  0  X  0  X  X  X  1  0  0  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+84x^20+116x^21+567x^22+524x^23+1122x^24+1438x^25+2420x^26+2766x^27+3890x^28+4866x^29+5223x^30+6660x^31+6015x^32+6536x^33+5388x^34+5024x^35+3964x^36+2948x^37+2353x^38+1288x^39+1178x^40+458x^41+400x^42+114x^43+126x^44+22x^45+33x^46+8x^47+4x^48

The gray image is a linear code over GF(2) with n=64, k=16 and d=20.
This code was found by Heurico 1.11 in 74.9 seconds.