The generator matrix

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

generates a code of length 13 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 8.

Homogenous weight enumerator: w(x)=1x^0+15x^8+36x^10+349x^12+256x^13+304x^14+44x^16+12x^18+7x^20

The gray image is a code over GF(2) with n=104, k=10 and d=32.
This code was found by Heurico 1.16 in 6.87e-008 seconds.