The generator matrix

 1  1  1  1  1  1  X 2X+2  X  X  1  1  1
 0  2  0  2  0  2  2  2  2  2 2X  2  0
 0  0 2X  0  0  0  0  0 2X 2X 2X  0  0
 0  0  0 2X  0  0  0  0 2X 2X  0 2X  0
 0  0  0  0 2X  0  0 2X  0 2X 2X  0  0
 0  0  0  0  0 2X  0 2X  0 2X  0 2X  0
 0  0  0  0  0  0 2X 2X 2X 2X  0  0  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+26x^8+16x^9+93x^10+64x^11+520x^12+608x^13+520x^14+64x^15+93x^16+16x^17+26x^18+1x^26

The gray image is a code over GF(2) with n=104, k=11 and d=32.
This code was found by Heurico 1.16 in -3.24e-008 seconds.