The generator matrix

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

generates a code of length 65 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+104x^61+646x^62+644x^63+648x^64+580x^65+376x^66+374x^67+300x^68+100x^69+160x^70+74x^71+65x^72+8x^73+9x^74+1x^76+4x^77+1x^78+1x^80

The gray image is a code over GF(2) with n=520, k=12 and d=244.
This code was found by Heurico 1.16 in 0.235 seconds.