The generator matrix

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

generates a code of length 23 over Z2[X]/(X^2) who´s minimum homogenous weight is 15.

Homogenous weight enumerator: w(x)=1x^0+62x^15+169x^16+216x^17+369x^18+494x^19+637x^20+782x^21+836x^22+926x^23+918x^24+870x^25+686x^26+518x^27+306x^28+170x^29+148x^30+44x^31+16x^32+10x^33+9x^34+4x^35+1x^36

The gray image is a linear code over GF(2) with n=46, k=13 and d=15.
This code was found by Heurico 1.16 in 1.92 seconds.