The generator matrix
1 1 1 1 X X 2 X
0 2X+2 0 2 2X 2X+2 2 0
0 0 2X+2 2 2 2X 2X+2 0
generates a code of length 8 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 6.
Homogenous weight enumerator: w(x)=1x^0+20x^6+68x^7+89x^8+56x^9+12x^10+4x^11+6x^12
The gray image is a code over GF(2) with n=64, k=8 and d=24.
This code was found by Heurico 1.16 in -6.48e-008 seconds.