The generator matrix

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

generates a code of length 64 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+115x^56+878x^57+2324x^58+4344x^59+7283x^60+10814x^61+14498x^62+16066x^63+18835x^64+15892x^65+14754x^66+10422x^67+7200x^68+4276x^69+1970x^70+876x^71+297x^72+134x^73+36x^74+32x^75+13x^76+6x^77+2x^79+2x^82+2x^83

The gray image is a code over GF(2) with n=512, k=17 and d=224.
This code was found by Heurico 1.16 in 139 seconds.