The generator matrix

 1  0  1  1  1 3X+2  1  1  2  1  1  1  1
 0  1 X+1 3X+2 2X+3  1  2 X+3  1  0 3X 2X+3 X+1
 0  0 2X  0  0 2X 2X  0  0 2X  0 2X  0
 0  0  0 2X  0 2X 2X 2X 2X  0  0  0  0
 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 10.

Homogenous weight enumerator: w(x)=1x^0+40x^10+144x^11+569x^12+544x^13+565x^14+144x^15+37x^16+2x^18+1x^20+1x^22

The gray image is a code over GF(2) with n=104, k=11 and d=40.
This code was found by Heurico 1.16 in 0.016 seconds.