The generator matrix

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

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+66x^12+188x^14+216x^16+272x^18+1066x^20+2348x^22+8192x^23+2222x^24+960x^26+390x^28+276x^30+119x^32+48x^34+14x^36+4x^38+2x^40

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 1.65 seconds.