The generator matrix

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

generates a code of length 57 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 50.

Homogenous weight enumerator: w(x)=1x^0+421x^50+1742x^51+3813x^52+6846x^53+10863x^54+14400x^55+17403x^56+19758x^57+17625x^58+15280x^59+10791x^60+6366x^61+3445x^62+1378x^63+590x^64+236x^65+54x^66+30x^67+8x^68+8x^69+8x^70+2x^71+2x^72+2x^73

The gray image is a code over GF(2) with n=456, k=17 and d=200.
This code was found by Heurico 1.16 in 126 seconds.