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.