The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  1  X  1  X  X  X  1  X  X  X  1
 0  X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  X  X
 0  0  X  0  0  0  0  0  0  0  0  0  0  0  0  X  0  0  0  X  X  X  X  X  X  0  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  X  X  0  0  0  X  0  0  X  X
 0  0  0  0  X  0  0  0  0  0  0  0  0  0  X  0  0  X  X  X  X  0  X  X  0  X  0  X  X  0  X
 0  0  0  0  0  X  0  0  0  0  0  0  0  0  X  0  X  0  X  X  0  X  0  X  X  X  0  X  0  X  X
 0  0  0  0  0  0  X  0  0  0  0  0  0  X  0  0  X  0  X  0  X  X  X  X  0  X  X  X  0  X  0
 0  0  0  0  0  0  0  X  0  0  0  0  0  X  0  0  0  X  0  X  X  X  0  0  X  X  X  X  X  X  0
 0  0  0  0  0  0  0  0  X  0  0  0  X  0  0  0  0  X  0  0  X  X  X  X  0  0  X  X  X  0  0
 0  0  0  0  0  0  0  0  0  X  0  0  X  0  0  0  X  0  0  X  X  0  0  X  0  X  X  0  X  X  0
 0  0  0  0  0  0  0  0  0  0  X  0  X  X  X  X  X  X  0  0  X  X  X  0  0  X  0  X  0  X  X
 0  0  0  0  0  0  0  0  0  0  0  X  X  X  X  X  0  0  0  X  0  X  0  X  X  X  X  X  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+232x^20+8x^22+631x^24+288x^26+1568x^28+1008x^30+2214x^32+672x^34+1098x^36+72x^38+313x^40+76x^44+9x^48+2x^52

The gray image is a linear code over GF(2) with n=62, k=13 and d=20.
This code was found by Heurico 1.16 in 76.6 seconds.