The generator matrix
1 0 0 1 1 1 1 1
0 1 0 1 X^2+X X^2+X+1 X+2 X^2
0 0 1 1 X+1 X X^2+X X
0 0 0 2 0 0 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+42x^5+537x^6+1496x^7+4045x^8+1492x^9+534x^10+40x^11+2x^12+2x^13+1x^14
The gray image is a code over GF(2) with n=64, k=13 and d=20.
This code was found by Heurico 1.16 in 0.032 seconds.