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.