The generator matrix
1 1 1 1 2 1 X^2+2 1
0 X 0 X X X^2+2 X 2
0 0 X X X^2 0 X^2+X X^2
0 0 0 2 0 2 2 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+26x^5+153x^6+360x^7+973x^8+356x^9+150x^10+24x^11+2x^12+2x^13+1x^14
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 3.81e-009 seconds.