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

generates a code of length 64 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+282x^61+373x^62+400x^63+209x^64+250x^65+224x^66+168x^67+25x^68+56x^69+26x^70+20x^71+4x^72+8x^77+1x^82+1x^88

The gray image is a code over GF(2) with n=512, k=11 and d=244.
This code was found by Heurico 1.16 in 0.219 seconds.