The generator matrix

 1  0  1  1  1 X^2+X  1  1  1  1 X^2+2 X+2  1
 0  1 X+1 X^2+X X^2+1  1 X^2+2 X+2 X^2+X+3  3  1  1  0
 0  0  2  2  0  2  2  0  0  2  2  0  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+28x^11+190x^12+72x^13+190x^14+28x^15+1x^16+2x^18

The gray image is a code over GF(2) with n=104, k=9 and d=44.
This code was found by Heurico 1.16 in -6.48e-008 seconds.