The generator matrix

 1  0  0  1  1  1  0  1  1  1  1  0  X  0  0  0  X  0  0  X  0  X  1
 0  1  0  1  0  1  1  0  X  1 X+1  1  1  0  1  1  1  1  1  1  0  0  0
 0  0  1  1  1  0  1  0  1 X+1  X  0  1  1  0  X  1 X+1  0  1  1  0  0
 0  0  0  X  0  0  0  0  0  X  0  X  X  X  0  X  0  X  0  0  0  X  0
 0  0  0  0  X  0  0  0  X  0  0  X  X  X  0  X  X  0  X  0  0  0  0
 0  0  0  0  0  X  0  0  0  0  X  X  X  X  X  0  0  X  X  0  0  0  0
 0  0  0  0  0  0  X  0  0  0  0  0  X  0  X  X  X  X  X  0  X  0  0
 0  0  0  0  0  0  0  X  X  X  X  X  0  0  0  X  0  0  0  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+61x^16+76x^17+115x^18+96x^19+146x^20+248x^21+190x^22+192x^23+192x^24+240x^25+148x^26+96x^27+110x^28+72x^29+50x^30+2x^32+4x^33+9x^34

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 0.115 seconds.