The generator matrix

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

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+44x^21+137x^22+292x^23+420x^24+584x^25+758x^26+910x^27+1154x^28+1336x^29+1578x^30+1750x^31+1644x^32+1472x^33+1276x^34+966x^35+733x^36+544x^37+312x^38+230x^39+139x^40+48x^41+33x^42+12x^43+5x^44+4x^45+1x^46+1x^50

The gray image is a linear code over GF(2) with n=62, k=14 and d=21.
This code was found by Heurico 1.10 in 3.81 seconds.