The generator matrix
1 1 1 1 1 1 1 1 X 0 X 1
0 X 0 X^2+X X^2 X^2+X X^2 X X^2+X X 0 0
0 0 X^2 X^2 X^2 0 0 X^2 0 X^2 0 0
generates a code of length 12 over Z2[X]/(X^3) who´s minimum homogenous weight is 10.
Homogenous weight enumerator: w(x)=1x^0+6x^10+18x^11+7x^12+28x^13+1x^14+2x^15+1x^18
The gray image is a linear code over GF(2) with n=48, k=6 and d=20.
This code was found by Heurico 1.16 in 0.0005 seconds.