The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X 1
0 2X+2 0 2X+2 0 2X+2 0 2X+2 0 2X+2 0 2X+2 0 2X+2 0 2X+2 2X 2 2X 2 2X 2 2X 2 2X 2 2X 2 2X 2 2X 2 2X+2 2X+2 2X+2 2X+2 2X+2 2X+2 2X+2 2X+2 0 2X 0 2X 0 2X 0 2X 0 2X 2 2 0 2X 2 0 2X 2 2 2 2 2 0 2X 0
0 0 2X 0 0 0 2X 0 0 2X 0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 0 0 0 0 0 0 0 0 0 0 0 0 2X 2X 2X 2X 0 0 0 0 2X 2X 2X 2X 0 0 2X 0 2X 2X 2X 2X 2X 2X 2X 0 0 0 0 0 0
0 0 0 2X 0 0 0 2X 2X 2X 2X 2X 2X 0 2X 0 0 0 0 0 2X 2X 2X 2X 2X 2X 2X 2X 0 0 0 0 0 0 2X 2X 2X 2X 0 0 0 0 2X 2X 2X 2X 0 0 2X 2X 0 2X 0 0 0 2X 2X 2X 2X 2X 0 0 0 0 0
0 0 0 0 2X 2X 2X 2X 2X 0 0 2X 0 2X 2X 0 0 0 2X 2X 2X 2X 0 0 0 0 2X 2X 2X 2X 0 0 0 2X 2X 0 0 2X 2X 0 2X 2X 2X 2X 0 0 0 0 0 0 0 2X 2X 2X 2X 2X 2X 2X 0 0 2X 0 0 0 0
generates a code of length 65 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 64.
Homogenous weight enumerator: w(x)=1x^0+31x^64+446x^65+32x^66+2x^97
The gray image is a code over GF(2) with n=520, k=9 and d=256.
This code was found by Heurico 1.16 in 0.234 seconds.