The generator matrix

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

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+20x^7+130x^8+96x^9+512x^10+136x^11+120x^12+4x^15+5x^16

The gray image is a code over GF(2) with n=80, k=10 and d=28.
This code was found by Heurico 1.16 in 0.015 seconds.