The generator matrix

 1  0  1  1  1  1  1  1  1  0
 0  1 X+1  0 X+1 X^2+3  0 X^2+X+2 X+1  1
 0  0 X^2  0  0  2 X^2 X^2 X^2+2  2
 0  0  0 X^2+2  2 X^2 X^2+2  2 X^2  0

generates a code of length 10 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 7.

Homogenous weight enumerator: w(x)=1x^0+48x^7+322x^8+720x^9+1920x^10+720x^11+312x^12+48x^13+5x^16

The gray image is a code over GF(2) with n=80, k=12 and d=28.
This code was found by Heurico 1.16 in 11.4 seconds.