The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+34x^9+77x^10+228x^11+187x^12+1012x^13+170x^14+232x^15+65x^16+26x^17+9x^18+4x^19+3x^20

The gray image is a code over GF(2) with n=104, k=11 and d=36.
This code was found by Heurico 1.16 in 0.016 seconds.