The generator matrix

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

generates a code of length 31 over Z2[X]/(X^2) who´s minimum homogenous weight is 24.

Homogenous weight enumerator: w(x)=1x^0+127x^24+206x^26+366x^28+342x^30+343x^32+298x^34+266x^36+50x^38+41x^40+8x^44

The gray image is a linear code over GF(2) with n=62, k=11 and d=24.
This code was found by Heurico 1.16 in 0.21 seconds.