The generator matrix
1 1 1 1 1 X X 1
0 X 0 X^2+X+2 2 X^2+X X^2+X+2 X^2+X+2
0 0 X^2+2 0 2 X^2 X^2 X^2
0 0 0 X^2+2 X^2+2 X^2 0 2
generates a code of length 8 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 5.
Homogenous weight enumerator: w(x)=1x^0+32x^5+140x^6+352x^7+1005x^8+352x^9+124x^10+32x^11+10x^12
The gray image is a code over GF(2) with n=64, k=11 and d=20.
This code was found by Heurico 1.16 in 6.87e-008 seconds.