The generator matrix

 1  0  0  0  0  0  0  1  1  1  1  1  1  X  X  0  X  1  0  0  1  1  1
 0  1  0  0  0  0  0  0  0  0  0  1  1  1  X  X  1  1  1  X  X  X  0
 0  0  1  0  0  0  0  0  1  X X+1  1  1  1  1  1  0 X+1  X  1 X+1  X  0
 0  0  0  1  0  0  0  0  1 X+1  1  0  X  1  1  X  0  0 X+1 X+1 X+1  0  0
 0  0  0  0  1  0  0  0  1  1  X  1  X  0  X X+1 X+1  1  X  X  X X+1  0
 0  0  0  0  0  1  0  1  1  0 X+1  X X+1  1 X+1  0 X+1  1  1  0  X  X  0
 0  0  0  0  0  0  1  1  X  0  1 X+1 X+1  X  1  0  1  X X+1  X  1  X  0
 0  0  0  0  0  0  0  X  0  X  X  X  0  X  0  X  X  X  0  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+64x^13+172x^14+312x^15+583x^16+928x^17+1336x^18+1908x^19+2466x^20+3128x^21+3676x^22+3634x^23+3522x^24+3176x^25+2564x^26+2032x^27+1332x^28+840x^29+552x^30+292x^31+158x^32+56x^33+20x^34+12x^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 1.16 in 21.2 seconds.