The generator matrix

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

generates a code of length 31 over Z2[X]/(X^2) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+26x^20+18x^21+126x^22+86x^23+241x^24+230x^25+370x^26+490x^27+551x^28+788x^29+708x^30+892x^31+743x^32+748x^33+593x^34+500x^35+376x^36+250x^37+219x^38+78x^39+101x^40+14x^41+28x^42+2x^43+7x^44+2x^46+2x^48+1x^50+1x^54

The gray image is a linear code over GF(2) with n=62, k=13 and d=20.
This code was found by Heurico 1.16 in 2.57 seconds.