The generator matrix

 1  0  0  1  1  1  X  1  1  1  1  1
 0  1  0  1 X^2+X X^2+X+1  1 X^2  X  0 X^2  0
 0  0  1  1 X^2+X+1 X^2+X  1  X  X  0  X  0
 0  0  0 X^2  0  0  0 X^2  0 X^2  0  0
 0  0  0  0 X^2  0  0 X^2 X^2  0  0  0
 0  0  0  0  0 X^2  0 X^2 X^2 X^2  0  0
 0  0  0  0  0  0 X^2 X^2  0 X^2 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+59x^6+8x^7+257x^8+232x^9+1223x^10+784x^11+3059x^12+784x^13+1233x^14+232x^15+258x^16+8x^17+45x^18+9x^20

The gray image is a linear code over GF(2) with n=48, k=13 and d=12.
This code was found by Heurico 1.16 in 0.0645 seconds.