The generator matrix

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

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+190x^11+148x^12+404x^13+80x^14+160x^15+27x^16+12x^17+2x^19

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 0.016 seconds.