The generator matrix

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

generates a code of length 59 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+499x^52+1816x^53+4110x^54+7210x^55+10509x^56+13748x^57+17966x^58+19038x^59+18315x^60+14564x^61+10570x^62+6520x^63+3524x^64+1542x^65+698x^66+278x^67+90x^68+40x^69+16x^70+10x^71+6x^72+2x^73

The gray image is a code over GF(2) with n=472, k=17 and d=208.
This code was found by Heurico 1.16 in 131 seconds.