The generator matrix

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

generates a code of length 59 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 51.

Homogenous weight enumerator: w(x)=1x^0+328x^51+1468x^52+3708x^53+7660x^54+13160x^55+20203x^56+28864x^57+35903x^58+38380x^59+36696x^60+30094x^61+20704x^62+12840x^63+6684x^64+3052x^65+1481x^66+576x^67+226x^68+50x^69+42x^70+8x^71+2x^72+8x^73+2x^74+4x^75

The gray image is a code over GF(2) with n=472, k=18 and d=204.
This code was found by Heurico 1.16 in 502 seconds.