The generator matrix

 1  0  0  0  1  1  1 X^2  1  1  X X^2+X+2  1
 0  1  0  0 X^2  3 X^2+X+1  1 X^2+X  1  1  1 X^2
 0  0  1  0 X^2+1  1  X X^2+1  3 X^2+X+1 X+1  2 X^2
 0  0  0  1  1 X^2 X+1 X^2+X+1 X+2 X^2+1  X X+3 X^2+X

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+222x^9+1447x^10+5468x^11+14658x^12+21828x^13+14922x^14+5360x^15+1347x^16+270x^17+7x^18+4x^19+2x^20

The gray image is a code over GF(2) with n=104, k=16 and d=36.
This code was found by Heurico 1.16 in 4.34 seconds.