The generator matrix

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

generates a code of length 13 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 11.

Homogenous weight enumerator: w(x)=1x^0+46x^11+86x^12+274x^13+63x^14+18x^15+9x^16+14x^17+1x^22

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 -3.24e-008 seconds.