The generator matrix

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

generates a code of length 13 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 11.

Homogenous weight enumerator: w(x)=1x^0+124x^11+201x^12+404x^13+168x^14+100x^15+13x^16+12x^17+1x^20

The gray image is a code over GF(2) with n=104, k=10 and d=44.
This code was found by Heurico 1.16 in -3.24e-008 seconds.