The generator matrix

 1  0  1  1  1 X^2+X  1  1  0  1  1  1
 0  1 X+1 X^2+X  1  1  0 X+1  1  0  0 X+1
 0  0 X^2  0  0  0  0  0  0 X^2 X^2  0
 0  0  0 X^2  0  0  0  0 X^2 X^2 X^2  0
 0  0  0  0 X^2  0  0  0 X^2  0  0 X^2
 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 X^2  0  0
 0  0  0  0  0  0  0 X^2  0 X^2 X^2 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+17x^6+8x^7+86x^8+136x^9+364x^10+1136x^11+596x^12+1136x^13+374x^14+136x^15+81x^16+8x^17+12x^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 0.0169 seconds.