The generator matrix

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

generates a code of length 23 over Z2[X]/(X^2) who´s minimum homogenous weight is 16.

Homogenous weight enumerator: w(x)=1x^0+48x^16+58x^17+122x^18+146x^19+172x^20+182x^21+165x^22+238x^23+184x^24+214x^25+172x^26+126x^27+100x^28+58x^29+50x^30+2x^31+7x^32+2x^34+1x^38

The gray image is a linear code over GF(2) with n=46, k=11 and d=16.
This code was found by Heurico 1.16 in 0.111 seconds.