The generator matrix

 1  1  1  1  1  1  1  1  X  1  X  1  1
 0  2  0 2X+2  0  0 2X+2 2X+2 2X 2X 2X 2X  0
 0  0  2 2X+2  0  2  2  0 2X+2 2X+2 2X+2 2X+2  0
 0  0  0 2X  0  0 2X  0 2X  0  0 2X  0
 0  0  0  0 2X  0  0  0 2X 2X  0 2X  0
 0  0  0  0  0 2X 2X 2X  0 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+33x^8+24x^9+31x^10+128x^11+59x^12+1488x^13+67x^14+128x^15+34x^16+24x^17+29x^18+1x^20+1x^22

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.