The generator matrix

 1  0  0  0  1  1  1  X  1  1  1  1
 0  1  0  0  X  1  1  1 X+1  1 X+1  0
 0  0  1  0 X+1  1  X X+1  1 X+1  1 X^2
 0  0  0  1  1 X^2+X X+1  1  1  1  1 X^2
 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  0 X^2  0  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+148x^7+599x^8+1604x^9+2699x^10+8488x^11+5585x^12+8488x^13+2693x^14+1604x^15+596x^16+148x^17+57x^18+3x^20

The gray image is a linear code over GF(2) with n=48, k=15 and d=12.
This code was found by Heurico 1.16 in 0.993 seconds.