The generator matrix

 1  1  1  1  1  X  1  1  1  X
 0  X  0 X^2+X+2  2 X^2+X X^2+2 X^2+X X^2+X+2 X^2+X+2
 0  0 X^2+2  0  2 X^2 X^2 X^2 X^2  0
 0  0  0 X^2+2 X^2+2 X^2 X^2 X^2+2  2 X^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+64x^7+98x^8+448x^9+832x^10+448x^11+88x^12+64x^13+5x^16

The gray image is a code over GF(2) with n=80, k=11 and d=28.
This code was found by Heurico 1.16 in 0.047 seconds.