The generator matrix

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

generates a code of length 13 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+15x^10+42x^11+16x^12+368x^13+15x^14+36x^15+15x^16+1x^18+2x^19+1x^22

The gray image is a code over GF(2) with n=104, k=9 and d=40.
This code was found by Heurico 1.16 in 6.87e-008 seconds.