The generator matrix

 1  1  1  1  X  X  X  1
 0 X^2+2  0 X^2  0 X^2 X^2+2  0
 0  0 X^2+2 X^2 X^2+2 X^2  0  0
 0  0  0  2  0  0  2  0
 0  0  0  0  2  0  2  0
 0  0  0  0  0  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+39x^4+32x^5+150x^6+96x^7+1407x^8+96x^9+164x^10+32x^11+25x^12+6x^14

The gray image is a code over GF(2) with n=64, k=11 and d=16.
This code was found by Heurico 1.16 in -6.48e-008 seconds.