The generator matrix

 1  0  0  0  1  1  1  0  1  1  1  1  X  X  X  1  1  1  0  0  1  1  1  X  0  X  1  0  1  1  1
 0  1  0  0  0  1  1  1  0  0 X+1 X+1  1  0  1  X X+1  0  X  X  0 X+1  X  1  X  1  0  X  0  0  0
 0  0  1  0  1  1  0  1  0  1  1  0  0  1  1  X  0 X+1  1  1  1  1  0  X  0  1  X  1 X+1  0  0
 0  0  0  1  1  0  1  1  1  0  1  0  1  1  0 X+1  0  1  0  1  X  0  X  X  1  X  0  0  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  0  X  X  0  0  0  0
 0  0  0  0  0  X  0  0  0  0  0  X  0  X  X  X  0  0  X  X  X  0  0  X  0  X  0  0  0  0  0
 0  0  0  0  0  0  X  0  0  0  X  X  0  X  X  0  0  X  X  0  X  0  X  0  0  X  0  X  X  0  0
 0  0  0  0  0  0  0  X  0  0  X  0  X  0  X  0  0  X  0  X  X  0  0  X  0  X  X  X  X  0  0
 0  0  0  0  0  0  0  0  X  0  X  X  X  X  0  0  X  X  0  X  X  X  X  0  0  0  X  X  X  X  X
 0  0  0  0  0  0  0  0  0  X  0  0  0  0  X  X  X  X  0  0  X  X  0  X  X  X  0  0  0  0  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+123x^20+276x^22+834x^24+1314x^26+2461x^28+3048x^30+3315x^32+2356x^34+1653x^36+628x^38+278x^40+58x^42+35x^44+4x^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 18.4 seconds.