The generator matrix

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

generates a code of length 12 over Z2[X]/(X^3) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+45x^4+10x^6+210x^8+120x^10+512x^11+2258x^12+512x^13+252x^14+45x^16+120x^18+1x^20+10x^22

The gray image is a linear code over GF(2) with n=48, k=12 and d=8.
This code was found by Heurico 1.16 in 0.023 seconds.