The generator matrix
1 1 1 1 1 1 1 1
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 0 0
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+10x^4+106x^8+10x^12+1x^16
The gray image is a code over GF(2) with n=32, k=7 and d=8.
This code was found by Heurico 1.16 in 0.00015 seconds.