The generator matrix

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

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+238x^20+54x^22+882x^24+906x^26+2772x^28+2972x^30+4205x^32+1876x^34+1686x^36+334x^38+370x^40+2x^42+72x^44+14x^48

The gray image is a linear code over GF(2) with n=62, k=14 and d=20.
This code was found by Heurico 1.16 in 46.2 seconds.