The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  X  X  X  1  1  1
 0  X  0  0  0  0  0  0  0  0  0  X  0  0  X  X  0  0  0  X  0  0  X  X  0  X  X  X  X  X  0
 0  0  X  0  0  0  0  0  0  0  0  X  X  X  X  X  0  X  0  X  0  X  X  0  X  0  X  0  0  X  X
 0  0  0  X  0  0  0  0  0  0  X  0  X  X  0  X  X  X  0  0  X  0  0  X  X  0  0  0  0  X  X
 0  0  0  0  X  0  0  0  0  0  X  0  0  X  X  X  X  0  X  X  0  X  X  X  X  X  0  X  X  0  X
 0  0  0  0  0  X  0  0  0  X  0  0  0  X  X  0  X  X  0  X  X  X  X  0  X  0  0  0  X  0  0
 0  0  0  0  0  0  X  0  0  X  0  0  X  0  0  X  X  X  X  X  0  X  X  X  X  X  X  0  0  0  0
 0  0  0  0  0  0  0  X  0  X  X  X  X  0  0  0  0  X  0  X  X  X  0  X  X  0  0  X  0  0  0
 0  0  0  0  0  0  0  0  X  X  X  X  0  0  X  X  X  0  0  X  0  0  0  0  X  X  X  0  0  0  X

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+113x^24+16x^26+204x^28+160x^30+269x^32+80x^34+125x^36+49x^40+6x^44+1x^52

The gray image is a linear code over GF(2) with n=62, k=10 and d=24.
This code was found by Heurico 1.16 in 31.1 seconds.