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.