The generator matrix

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

generates a code of length 13 over Z4[X]/(X^2+2X+2) 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 6.87e-008 seconds.