The generator matrix
1 0 0 1 1 1 X^2+X X^2+2 1 1 1 1 1
0 1 0 1 X X^2+X+1 1 1 X X+2 X^2+X+3 0 X^2+2
0 0 1 1 X^2+1 X X+1 X 1 X X^2 X^2+2 X^2
0 0 0 X^2+2 X^2 2 0 X^2 0 X^2+2 X^2+2 2 X^2
generates a code of length 13 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 9.
Homogenous weight enumerator: w(x)=1x^0+76x^9+358x^10+1408x^11+3140x^12+6380x^13+3204x^14+1404x^15+331x^16+72x^17+6x^18+4x^19
The gray image is a code over GF(2) with n=104, k=14 and d=36.
This code was found by Heurico 1.16 in 0.313 seconds.