The generator matrix

 1  0  0  1  1  1  X  X
 0  1  0  X  1 X+3  1  0
 0  0  1  1 X+3 X+2  1  0
 0  0  0  2  0  0  0  2
 0  0  0  0  2  0  0  2
 0  0  0  0  0  2  0  2
 0  0  0  0  0  0  2  2

generates a code of length 8 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 4.

Homogenous weight enumerator: w(x)=1x^0+84x^4+320x^5+800x^6+1728x^7+2326x^8+1728x^9+800x^10+320x^11+84x^12+1x^16

The gray image is a code over GF(2) with n=32, k=13 and d=8.
This code was found by Heurico 1.16 in 0.032 seconds.