The generator matrix

 1  1  1  1  1  1  1  1  1  1 2X+2  X  1
 0  X  2 3X+2  0 3X+2  0 3X+2 2X X+2  2 3X+2  0
 0  0 2X  0  0 2X 2X 2X 2X  0  0  0  0
 0  0  0 2X 2X 2X 2X  0  0  0 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+18x^10+50x^11+94x^12+190x^13+91x^14+46x^15+17x^16+2x^17+2x^18+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.