The generator matrix

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

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+318x^11+276x^12+916x^13+208x^14+288x^15+27x^16+12x^17+2x^19

The gray image is a code over GF(2) with n=104, k=11 and d=44.
This code was found by Heurico 1.16 in 3.49 seconds.