The generator matrix

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

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+58x^21+159x^22+236x^23+416x^24+550x^25+792x^26+962x^27+1133x^28+1422x^29+1529x^30+1684x^31+1628x^32+1464x^33+1260x^34+1008x^35+774x^36+562x^37+325x^38+192x^39+130x^40+34x^41+28x^42+14x^43+13x^44+6x^45+3x^46+1x^48

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 20.8 seconds.