The generator matrix

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

generates a code of length 23 over Z2[X]/(X^2) who´s minimum homogenous weight is 14.

Homogenous weight enumerator: w(x)=1x^0+19x^14+84x^15+175x^16+254x^17+387x^18+452x^19+600x^20+754x^21+866x^22+962x^23+851x^24+814x^25+637x^26+482x^27+385x^28+214x^29+134x^30+66x^31+33x^32+12x^33+4x^34+2x^35+3x^36+1x^38

The gray image is a linear code over GF(2) with n=46, k=13 and d=14.
This code was found by an older version of Heurico in 0 seconds.