The generator matrix

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

generates a code of length 8 over Z4[X]/(X^2+2) 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 3.81e-009 seconds.