The generator matrix
1 1 1 1 1 1 1 1
0 2 0 0 0 0 0 0
0 0 2 0 0 0 0 0
0 0 0 2 0 0 0 0
0 0 0 0 2 0 0 0
0 0 0 0 0 2 0 0
0 0 0 0 0 0 2 0
0 0 0 0 0 0 0 2
generates a code of length 8 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 2.
Homogenous weight enumerator: w(x)=1x^0+8x^2+28x^4+56x^6+1862x^8+56x^10+28x^12+8x^14+1x^16
The gray image is a code over GF(2) with n=64, k=11 and d=8.
This code was found by Heurico 1.16 in 0.016 seconds.