The generator matrix
1 1 1 1 1 1 1 1
0 X 2 X+2 X^2+2 X^2 X^2+X X^2+X+2
generates a code of length 8 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 8.
Homogenous weight enumerator: w(x)=1x^0+126x^8+1x^16
The gray image is a code over GF(2) with n=64, k=7 and d=32.
This code was found by Heurico 1.16 in -6.48e-008 seconds.