The generator matrix

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

generates a code of length 8 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+239x^4+1864x^5+12530x^6+60192x^7+112639x^8+59888x^9+12652x^10+1952x^11+177x^12+8x^13+2x^14

The gray image is a code over GF(2) with n=64, k=18 and d=16.
This code was found by Heurico 1.16 in 17.3 seconds.