The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  X  1  1  1
 0  X  0  0  0  0  0  0  0  0  0  X  0  0  X  X  0  X  X  X  0  X  0
 0  0  X  0  0  0  0  0  0  0  0  X  X  X  X  X  X  X  0  0  0  0  0
 0  0  0  X  0  0  0  0  0  0  X  0  X  X  0  X  X  0  X  0  X  0  0
 0  0  0  0  X  0  0  0  0  0  X  0  0  X  X  X  0  X  0  X  X  0  0
 0  0  0  0  0  X  0  0  0  X  0  0  0  X  X  0  X  X  X  0  X  0  0
 0  0  0  0  0  0  X  0  0  X  0  0  X  0  0  X  X  X  0  X  X  0  0
 0  0  0  0  0  0  0  X  0  X  X  X  X  0  0  0  X  X  X  0  0  0  0
 0  0  0  0  0  0  0  0  X  X  X  X  0  0  X  X  X  0  0  0  X  0  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+97x^16+61x^18+32x^19+33x^20+128x^21+19x^22+192x^23+90x^24+128x^25+118x^26+32x^27+30x^28+42x^30+4x^32+13x^34+1x^36+3x^38

The gray image is a linear code over GF(2) with n=46, k=10 and d=16.
This code was found by Heurico 1.16 in 0.0416 seconds.