The generator matrix
1 1 1 1 X X X X
0 2 0 2 2 0 2 0
generates a code of length 8 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 8.
Homogenous weight enumerator: w(x)=1x^0+13x^8+2x^12
The gray image is a code over GF(2) with n=32, k=4 and d=16.
This code was found by Heurico 1.16 in 0.000136 seconds.