The generator matrix

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

generates a code of length 31 over Z2[X]/(X^2) who´s minimum homogenous weight is 20.

Homogenous weight enumerator: w(x)=1x^0+60x^20+334x^22+873x^24+1396x^26+2379x^28+2912x^30+3454x^32+2292x^34+1622x^36+674x^38+303x^40+72x^42+11x^44+1x^48

The gray image is a linear code over GF(2) with n=62, k=14 and d=20.
This code was found by an older version of Heurico in 0 seconds.