The generator matrix

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

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+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 0.015 seconds.