The generator matrix

 1  1  1  1  1  1  1  1  X  0  X  1
 0  X  2 3X+2 2X X+2 2X+2 3X 3X+2  X 3X  0

generates a code of length 12 over Z4[X]/(X^2+2X+2) 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 3.81e-009 seconds.