The generator matrix

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

generates a code of length 9 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 6.

Homogenous weight enumerator: w(x)=1x^0+105x^6+516x^7+1493x^8+3972x^9+1494x^10+492x^11+106x^12+12x^13+1x^14

The gray image is a code over GF(2) with n=72, k=13 and d=24.
This code was found by Heurico 1.16 in 0.047 seconds.