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.