The generator matrix
1 1 X 1
0 2X+2 2X+2 0
0 0 2X 0
generates a code of length 4 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 2.
Homogenous weight enumerator: w(x)=1x^0+6x^2+16x^3+82x^4+16x^5+6x^6+1x^8
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 6.87e-008 seconds.