The generator matrix
1 1 1 1 1 1 1 1 X X X^2 1
0 X 0 0 0 0 0 X^2 X^2+X X^2+X X^2 X^2+X
0 0 X 0 0 X^2 X^2+X X X^2+X 0 X X^2+X
0 0 0 X 0 X^2+X X^2+X X 0 X^2 X^2 0
0 0 0 0 X X X^2 X^2+X X^2+X 0 X^2+X X^2+X
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+86x^8+200x^9+76x^10+480x^11+144x^12+784x^13+168x^14+32x^15+25x^16+40x^17+12x^18
The gray image is a linear code over GF(2) with n=48, k=11 and d=16.
This code was found by Heurico 1.16 in 0.0202 seconds.