The generator matrix

 1  1  1  1  X  X  X  1
 0  X  0 X^2+X+2 X^2+X X^2+X X^2+X  0
 0  0 X^2+2 X^2  0  0  2  0
 0  0  0  2  0  2  2  0
 0  0  0  0  2  2  0  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+12x^4+90x^5+75x^6+296x^7+1101x^8+292x^9+82x^10+88x^11+6x^12+2x^13+3x^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 6.87e-008 seconds.