The generator matrix

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

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+18x^4+20x^5+64x^6+44x^7+730x^8+44x^9+64x^10+20x^11+18x^12+1x^16

The gray image is a code over GF(2) with n=64, k=10 and d=16.
This code was found by Heurico 1.16 in 3.62e-008 seconds.