The generator matrix

 1  1  1  1  X  1  1  1
 0  X  0 X^2+X+2 X^2+X X^2 X^2+X  0
 0  0 X^2+2 X^2  2 X^2  0  0
 0  0  0  2  2  2  2  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+14x^5+41x^6+212x^7+493x^8+208x^9+38x^10+12x^11+2x^12+2x^13+1x^14

The gray image is a code over GF(2) with n=64, k=10 and d=20.
This code was found by Heurico 1.16 in 3.81e-009 seconds.