The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+26x^8+12x^10+32x^11+24x^12+832x^13+28x^14+32x^15+13x^16+20x^18+4x^22

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 0.015 seconds.