The generator matrix

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

generates a code of length 65 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+89x^56+692x^57+2270x^58+4588x^59+8450x^60+14284x^61+19746x^62+28400x^63+33734x^64+36620x^65+34000x^66+29712x^67+20698x^68+13700x^69+7772x^70+4256x^71+1835x^72+736x^73+318x^74+116x^75+82x^76+16x^77+18x^78+5x^80+4x^82+2x^84

The gray image is a code over GF(2) with n=520, k=18 and d=224.
This code was found by Heurico 1.16 in 579 seconds.