The generator matrix

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

generates a code of length 13 over Z4[X]/(X^3+2,2X) 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 0.015 seconds.