The generator matrix
1 1 1 1 1 1 1 1 X 0 X 1
0 X X^2+2 X^2+X 2 X^2+X+2 X^2 X+2 X^2+X X X+2 0
generates a code of length 12 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 11.
Homogenous weight enumerator: w(x)=1x^0+36x^11+52x^12+36x^13+1x^14+1x^16+1x^18
The gray image is a code over GF(2) with n=96, k=7 and d=44.
This code was found by Heurico 1.16 in 0 seconds.