The generator matrix

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

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+84x^10+368x^11+830x^12+1580x^13+782x^14+344x^15+81x^16+12x^17+14x^18

The gray image is a code over GF(2) with n=104, k=12 and d=40.
This code was found by Heurico 1.16 in 0.032 seconds.