The generator matrix

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

generates a code of length 6 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+21x^4+66x^5+85x^6+60x^7+18x^8+2x^9+3x^10

The gray image is a code over GF(2) with n=24, k=8 and d=8.
This code was found by Heurico 1.16 in 0.000187 seconds.