The generator matrix

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

generates a code of length 31 over Z2[X]/(X^2) who´s minimum homogenous weight is 21.

Homogenous weight enumerator: w(x)=1x^0+46x^21+137x^22+288x^23+429x^24+584x^25+730x^26+926x^27+1182x^28+1328x^29+1583x^30+1694x^31+1609x^32+1530x^33+1296x^34+986x^35+736x^36+536x^37+323x^38+186x^39+129x^40+70x^41+22x^42+16x^43+10x^44+2x^45+5x^46

The gray image is a linear code over GF(2) with n=62, k=14 and d=21.
This code was found by Heurico 1.16 in 23.1 seconds.