The generator matrix
1 0 0 0 0 1 1 1 1 1 1 1
0 1 0 0 0 1 0 X X+1 1 X^2 0
0 0 1 0 0 1 X X+1 X+1 X 1 0
0 0 0 1 0 1 X+1 X 1 X X^2+X+1 0
0 0 0 0 1 1 X^2+1 0 X X^2+1 X^2+X+1 0
0 0 0 0 0 X^2 X^2 X^2 0 0 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+95x^6+538x^7+1306x^8+3834x^9+7421x^10+12580x^11+14062x^12+12388x^13+7497x^14+3954x^15+1265x^16+482x^17+91x^18+16x^19+6x^20
The gray image is a linear code over GF(2) with n=48, k=16 and d=12.
This code was found by Heurico 1.13 in 0.969 seconds.