The generator matrix

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

generates a code of length 8 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 5.

Homogenous weight enumerator: w(x)=1x^0+32x^5+140x^6+352x^7+1005x^8+352x^9+124x^10+32x^11+10x^12

The gray image is a code over GF(2) with n=64, k=11 and d=20.
This code was found by Heurico 1.16 in 6.87e-008 seconds.