The generator matrix

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

generates a code of length 31 over Z2[X]/(X^2) who´s minimum homogenous weight is 23.

Homogenous weight enumerator: w(x)=1x^0+54x^23+138x^24+156x^25+229x^26+286x^27+324x^28+342x^29+303x^30+374x^31+361x^32+366x^33+360x^34+262x^35+208x^36+146x^37+97x^38+44x^39+24x^40+14x^41+2x^42+4x^43+1x^50

The gray image is a linear code over GF(2) with n=62, k=12 and d=23.
This code was found by an older version of Heurico in 0 seconds.