The generator matrix

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

generates a code of length 13 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 9.

Homogenous weight enumerator: w(x)=1x^0+56x^9+119x^10+412x^11+780x^12+1368x^13+779x^14+416x^15+99x^16+48x^17+13x^18+4x^19+1x^22

The gray image is a code over GF(2) with n=104, k=12 and d=36.
This code was found by Heurico 1.16 in 0.156 seconds.