The generator matrix

 1  1  1  1  1  1 X^2  1
 0 X^2+2  0 X^2+2  0  2  2 X^2+2
 0  0  2  0  0  2  0  2
 0  0  0  2  2  2  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+9x^6+56x^7+141x^8+32x^9+6x^10+8x^11+2x^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 1.05e-007 seconds.