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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  1  X  1  X  X X^2+2  1  1  1  2  1  1  1  1  1
 0  X  0  X  2  0 X+2  X X^2 X^2+X X^2 X^2+X X^2+2 X^2+X+2 X^2 X^2+X  0  2 X+2 X+2  0 X^2 X+2 X^2+X X^2 X^2+X+2  2 X^2+X X^2+2 X^2+X X^2+2  X  0 X^2  X  X X^2 X+2  2 X+2 X^2+2 X+2 X^2+2 X^2+2 X^2+X X^2+X+2  0 X^2+X+2  2 X^2+2 X^2 X^2+X X^2+X+2 X+2  X X^2+2  0 X^2+X  X  2  X X^2 X^2+2  X
 0  0  X  X X^2 X^2+X X^2+X X^2 X^2 X^2+X+2  X X^2+2  0 X+2 X^2+X  2  0 X^2+X+2 X^2+X X^2+2 X^2+2 X^2+X X+2 X^2+2 X^2+2 X^2+X+2 X+2  2  2 X+2 X+2  0  2 X+2 X+2  2  X  2 X^2+2 X^2+X+2 X^2+X X^2 X^2+2 X^2+2 X^2+X+2 X^2+X X+2  2  X  0 X^2+X+2  X X^2+2  0  0 X^2+X+2 X^2 X^2+X X^2+2  0 X^2+X X^2 X^2+X+2  X
 0  0  0  2  2  2  0  2  0  2  2  0  2  0  0  2  2  0  2  0  0  2  0  2  2  0  2  0  0  2  0  2  0  2  2  0  0  2  2  0  0  2  2  0  0  2  2  0  2  0  0  2  2  2  2  2  2  2  0  2  0  2  0  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+191x^60+16x^61+316x^62+368x^63+339x^64+368x^65+240x^66+16x^67+127x^68+52x^70+12x^72+1x^76+1x^116

The gray image is a code over GF(2) with n=512, k=11 and d=240.
This code was found by Heurico 1.16 in 0.297 seconds.