The generator matrix

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

generates a code of length 12 over Z2[X]/(X^3) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+37x^6+174x^8+128x^9+600x^10+384x^11+1444x^12+384x^13+610x^14+128x^15+169x^16+32x^18+4x^20+1x^22

The gray image is a linear code over GF(2) with n=48, k=12 and d=12.
This code was found by Heurico 1.16 in 0.0286 seconds.