The generator matrix

 1  1  1  1  1  1  X  1  0  1  X  1  1  0  1  X  1  X  1  1  1  1  1
 0  X  0 X^2+X  0 X^2+X  X  0  X X^2+X  X  0 X^2+X  X  0 X^2+X X^2+X X^2+X X^2+X X^2+X X^2+X  0  0
 0  0 X^2  0  0  0  0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2  0  0
 0  0  0 X^2  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2 X^2 X^2 X^2  0  0  0  0
 0  0  0  0 X^2  0  0  0  0  0  0  0 X^2 X^2 X^2  0  0 X^2 X^2 X^2 X^2  0  0
 0  0  0  0  0 X^2  0  0  0  0  0  0 X^2  0 X^2 X^2  0  0 X^2  0 X^2  0  0
 0  0  0  0  0  0 X^2  0  0  0  0 X^2  0  0 X^2 X^2 X^2  0 X^2 X^2 X^2  0  0
 0  0  0  0  0  0  0 X^2  0  0  0 X^2  0 X^2 X^2  0  0  0 X^2 X^2  0  0  0
 0  0  0  0  0  0  0  0 X^2  0  0 X^2 X^2  0 X^2  0 X^2 X^2 X^2  0  0  0  0
 0  0  0  0  0  0  0  0  0 X^2  0 X^2 X^2 X^2  0  0 X^2  0 X^2  0 X^2  0  0
 0  0  0  0  0  0  0  0  0  0 X^2 X^2 X^2  0  0 X^2  0 X^2 X^2 X^2  0  0  0

generates a code of length 23 over Z2[X]/(X^3) who´s minimum homogenous weight is 12.

Homogenous weight enumerator: w(x)=1x^0+40x^12+164x^14+32x^15+182x^16+192x^17+224x^18+768x^19+592x^20+2880x^21+824x^22+4544x^23+784x^24+2880x^25+688x^26+768x^27+344x^28+192x^29+68x^30+32x^31+89x^32+80x^34+16x^36

The gray image is a linear code over GF(2) with n=92, k=14 and d=24.
This code was found by Heurico 1.16 in 1.67 seconds.