The generator matrix

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

generates a code of length 12 over Z2[X]/(X^3) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+29x^8+64x^9+99x^10+190x^11+254x^12+204x^13+102x^14+48x^15+20x^16+4x^17+7x^18+2x^19

The gray image is a linear code over GF(2) with n=48, k=10 and d=16.
This code was found by Heurico 1.16 in 0.00486 seconds.