The generator matrix

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

generates a code of length 12 over Z2[X]/(X^3) who´s minimum homogenous weight is 7.

Homogenous weight enumerator: w(x)=1x^0+60x^7+129x^8+146x^9+606x^10+294x^11+1581x^12+324x^13+660x^14+152x^15+78x^16+42x^17+14x^18+6x^19+3x^20

The gray image is a linear code over GF(2) with n=48, k=12 and d=14.
This code was found by Heurico 1.16 in 0.133 seconds.