The generator matrix

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

generates a code of length 64 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+418x^58+1176x^59+2128x^60+2728x^61+3512x^62+4572x^63+4332x^64+4296x^65+3336x^66+2812x^67+1698x^68+816x^69+544x^70+172x^71+110x^72+64x^73+46x^74+4x^75+2x^76+1x^80

The gray image is a code over GF(2) with n=512, k=15 and d=232.
This code was found by Heurico 1.16 in 9.56 seconds.