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+2 X^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+24x^5+248x^6+754x^7+2061x^8+726x^9+248x^10+30x^11+2x^12+2x^13

The gray image is a code over GF(2) with n=64, k=12 and d=20.
This code was found by Heurico 1.16 in 0.016 seconds.