The generator matrix

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

generates a code of length 64 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 60.

Homogenous weight enumerator: w(x)=1x^0+80x^60+580x^61+804x^62+648x^63+489x^64+456x^65+368x^66+220x^67+136x^68+112x^69+84x^70+76x^71+15x^72+20x^73+6x^76+1x^80

The gray image is a code over GF(2) with n=512, k=12 and d=240.
This code was found by Heurico 1.16 in 0.234 seconds.