The generator matrix

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

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+76x^9+358x^10+1408x^11+3140x^12+6380x^13+3204x^14+1404x^15+331x^16+72x^17+6x^18+4x^19

The gray image is a code over GF(2) with n=104, k=14 and d=36.
This code was found by Heurico 1.16 in 0.313 seconds.