The generator matrix

1 0 0 0 0 1 1 1 X 1 1 0 1 X 1 X 1 1 1 1 0 0 0 1 1 1 X 1 1 1 1
0 1 0 0 0 0 0 0 0 1 1 1 X X 1 0 X X+1 X+1 1 1 0 1 X+1 X+1 1 1 X 0 X 0
0 0 1 0 0 0 1 1 1 0 X X 0 X 1 1 X+1 X X+1 X X+1 1 0 X+1 1 1 0 X X+1 0 0
0 0 0 1 0 1 0 X+1 1 1 0 X+1 0 1 X 1 X X 0 1 0 1 X X+1 1 0 X X+1 X 1 X+1
0 0 0 0 1 1 X+1 X 1 X 1 1 0 0 0 X+1 0 X 1 X+1 0 0 X+1 X 0 X X X+1 X 1 X+1
0 0 0 0 0 X X 0 0 0 0 X X X X X 0 X X X X X X X 0 0 X 0 X 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+69x^24+94x^25+116x^26+162x^27+168x^28+156x^29+155x^30+198x^31+185x^32+194x^33+149x^34+126x^35+106x^36+66x^37+53x^38+26x^39+13x^40+7x^42+2x^44+2x^45

The gray image is a linear code over GF(2) with n=62, k=11 and d=24.
This code was found by Heurico 1.10 in 0.078 seconds.