The generator matrix

 1  1  1  1  1  1  1  1
 0 X^2+2  0 X^2  2  2 X^2+2 X^2
 0  0  2  0  2  0  2  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 1.05e-007 seconds.