The generator matrix
1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 X 1 0 1 1 X X^2+2 1 1 X 2 1 1 X X^2 X X X X 1 1 1 1 X 0 1 1 1 1 X X^2+2 X X 2 X^2 X^2 0 X^2 2 X X 1 1 1 1 1
0 X X^2+2 X^2+X 2 X^2+X+2 X^2 X+2 0 X^2+X X^2+2 X+2 2 X^2+X+2 X^2 X 0 X^2+X X^2+X X X^2+2 X+2 X+2 X 2 X^2+X+2 X^2+X+2 X X^2 X X X 0 X^2+2 2 X^2 0 X^2+X X^2+2 X+2 X^2+X X 2 X^2 X^2+X+2 X X+2 X X^2+X+2 X X X X^2+2 X^2 X^2 X^2 0 2 X^2+X X^2+X+2 0 2 0
generates a code of length 63 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 62.
Homogenous weight enumerator: w(x)=1x^0+6x^62+104x^63+4x^64+4x^65+2x^67+3x^68+1x^70+2x^71+1x^74
The gray image is a code over GF(2) with n=504, k=7 and d=248.
This code was found by Heurico 1.16 in 0.125 seconds.