The generator matrix

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

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+55x^6+52x^7+115x^8+128x^9+475x^10+348x^11+1789x^12+288x^13+453x^14+172x^15+136x^16+32x^17+41x^18+4x^19+7x^20

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 0.0247 seconds.