The generator matrix

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

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+34x^13+133x^14+256x^15+574x^16+750x^17+1316x^18+1900x^19+2518x^20+3276x^21+3615x^22+3896x^23+3624x^24+3380x^25+2648x^26+1872x^27+1332x^28+722x^29+459x^30+264x^31+137x^32+30x^33+20x^34+4x^35+6x^36+1x^38

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 17.3 seconds.