The generator matrix

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

generates a code of length 8 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 7.

Homogenous weight enumerator: w(x)=1x^0+80x^7+93x^8+80x^9+2x^12

The gray image is a code over GF(2) with n=64, k=8 and d=28.
This code was found by Heurico 1.16 in -1.01e-007 seconds.