The generator matrix
1 1 1 1 1 1 X X
0 X 0 0 0 X 2 2
0 0 X 0 X X X 2
0 0 0 X X 0 0 2
0 0 0 0 2 0 2 2
0 0 0 0 0 2 2 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+83x^4+230x^6+256x^7+903x^8+256x^9+244x^10+69x^12+6x^14
The gray image is a code over GF(2) with n=32, k=11 and d=8.
This code was found by Heurico 1.16 in 0.00378 seconds.