The generator matrix
1 0 0 0 1 1 1 X+2 1 1
0 1 0 0 X^2 X^2+1 1 1 X^2+2 X+2
0 0 1 0 X^2+1 1 X X+1 X^2+X+1 X^2
0 0 0 1 1 X X+1 X^2+1 X^2+X+1 X^2+X+1
0 0 0 0 2 0 2 0 0 2
generates a code of length 10 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 6.
Homogenous weight enumerator: w(x)=1x^0+245x^6+1596x^7+8336x^8+30176x^9+50391x^10+30104x^11+8396x^12+1600x^13+211x^14+12x^15+3x^16+1x^18
The gray image is a code over GF(2) with n=80, k=17 and d=24.
This code was found by Heurico 1.16 in 17 seconds.