The generator matrix

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

generates a code of length 8 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+8x^6+56x^7+126x^8+56x^9+7x^10+1x^12+1x^14

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 0 seconds.