The generator matrix

 1  0  0  0  1  1  1  1  1 X^2 X^2  1
 0  1  0  0  1  X X^2 X^2+X+1  0  1  0  0
 0  0  1  0  1  0 X+1  0  1  X X^2  0
 0  0  0  1  1 X+1  0  X  1 X+1  1  0
 0  0  0  0  X  X X^2+X X^2  0 X^2 X^2+X  0
 0  0  0  0  0 X^2 X^2 X^2 X^2  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+58x^6+206x^7+775x^8+1794x^9+3784x^10+6264x^11+7075x^12+6068x^13+3922x^14+1838x^15+720x^16+202x^17+44x^18+12x^19+5x^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 1.18 seconds.