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.