The generator matrix

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

generates a code of length 58 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+386x^53+1022x^54+1664x^55+2069x^56+2194x^57+2344x^58+2104x^59+1719x^60+1310x^61+758x^62+380x^63+227x^64+116x^65+40x^66+28x^67+7x^68+8x^69+4x^70+1x^72+2x^73

The gray image is a code over GF(2) with n=464, k=14 and d=212.
This code was found by Heurico 1.16 in 2.3 seconds.