The generator matrix

 1  0  0  0  0  1  1  1  0  1  1  X  1  0  X  1  X  1  X  X  1  1  1  1  1  1  X  0  1  1  1
 0  1  0  0  0  0  0  0  0  1 X+1  1  1  1  X  X  1 X+1  X  1 X+1 X+1  0  X  0  1  1  X X+1  0  0
 0  0  1  0  0  0  1  1  1  1  1  0  X  1  1  X X+1 X+1  0 X+1  X  0 X+1 X+1  X X+1  0  0  0  X  0
 0  0  0  1  0  1  1  0  1  0  0  1  1  1  X  0  1  1  1  X X+1  X  0 X+1 X+1  1 X+1  X  1  X  0
 0  0  0  0  1  1  0  1  1  0  1  0  X  X X+1 X+1 X+1  0  1  0  1  0  0 X+1  X  1  X  1 X+1 X+1  0
 0  0  0  0  0  X  0  0  0  0  0  0  X  0  X  X  X  0  0  X  0  0  X  0  0  X  0  X  X  X  0
 0  0  0  0  0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  0  X  0  0  X  X
 0  0  0  0  0  0  0  X  0  0  0  0  0  0  0  0  X  X  X  X  0  X  0  X  0  X  0  X  X  X  X
 0  0  0  0  0  0  0  0  X  0  X  X  X  X  X  0  X  0  0  X  0  X  X  X  X  0  X  X  0  X  0
 0  0  0  0  0  0  0  0  0  X  X  0  0  X  0  X  X  X  0  0  X  0  0  X  0  X  0  X  0  X  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+73x^20+132x^21+324x^22+416x^23+801x^24+1038x^25+1394x^26+1922x^27+2430x^28+2896x^29+3162x^30+3416x^31+3133x^32+3092x^33+2492x^34+2028x^35+1453x^36+924x^37+736x^38+376x^39+273x^40+110x^41+82x^42+34x^43+28x^44+2x^46

The gray image is a linear code over GF(2) with n=62, k=15 and d=20.
This code was found by Heurico 1.16 in 36.4 seconds.