The generator matrix

 1  0  1  1  1  X  1  1
 0  1  1 X^2+2 X+3  X X+2  0
 0  0  X X^2+X X^2  X X^2+X  0

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+48x^5+127x^6+386x^7+934x^8+380x^9+113x^10+50x^11+9x^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 -3.24e-008 seconds.