The generator matrix

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

generates a code of length 13 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+157x^10+844x^11+1608x^12+3006x^13+1594x^14+802x^15+151x^16+18x^17+9x^18+2x^19

The gray image is a code over GF(2) with n=104, k=13 and d=40.
This code was found by Heurico 1.16 in 0.078 seconds.