The generator matrix

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

generates a code of length 23 over Z2[X]/(X^2) who´s minimum homogenous weight is 13.

Homogenous weight enumerator: w(x)=1x^0+54x^13+187x^14+332x^15+555x^16+914x^17+1304x^18+1952x^19+2562x^20+3060x^21+3646x^22+3610x^23+3482x^24+3276x^25+2536x^26+1992x^27+1428x^28+822x^29+495x^30+296x^31+162x^32+66x^33+24x^34+8x^35+2x^36+2x^39

The gray image is a linear code over GF(2) with n=46, k=15 and d=13.
This code was found by Heurico 1.11 in 7.82 seconds.