The generator matrix

 1  0  1  1  1  X  1  1 X^2+X  1  1  X X^2+X+2 X^2  1  1  1  1 X^2+X+2  1  1  1 X^2  1  1  X  1  1  1  2  1  1 X^2+X+2  1  1  1  1 X+2  1  1  1  1  1  1  1  1  1  2 X^2  1  1  1  1 X^2+2  1  2 X^2+2  1  1  1 X^2  1 X+2  0  1
 0  1  1 X^2 X+1  1  X  3  1 X^2+X X+3  1  1  1  0 X^2+X+3 X+2 X^2+1  1 X^2+X+3 X+2 X+3  1 X+3 X+2  1 X^2+X  0 X^2+3  1 X^2+X+1 X^2+X  1 X^2+2 X^2+X+2 X^2+1 X^2+X+3  1 X^2 X^2  2  2  3 X^2+X  2  2 X^2  1  1  3  X  2 X^2+2  1  X  1  1 X^2+1 X^2+1 X+1  X X^2+X+2  1  0 X^2+3
 0  0  X X+2  2 X+2 X+2  2  0  0  X X^2+X X^2+2 X^2 X^2+2 X^2+X+2 X^2 X^2+X+2 X+2  2 X^2+X X^2+2 X+2 X^2+X  0  0 X^2+2 X^2+X X^2+2 X^2+X+2 X^2 X^2+X+2 X^2+X+2 X^2+X+2 X+2 X^2+X  X X^2 X^2+2  0  X X+2 X^2+2  2  0 X^2+X+2 X^2 X^2 X^2+X+2 X^2+X+2 X^2+X+2 X^2 X^2+X X^2+2 X^2+2 X^2+X  X X^2  2  0 X+2  2 X^2+X  X X^2+X

generates a code of length 65 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+428x^62+212x^63+389x^64+112x^65+314x^66+168x^67+348x^68+16x^69+32x^70+4x^71+13x^72+9x^74+1x^88+1x^90

The gray image is a code over GF(2) with n=520, k=11 and d=248.
This code was found by Heurico 1.16 in 0.297 seconds.