The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+402x^53+934x^54+1748x^55+2076x^56+2092x^57+2591x^58+1894x^59+1790x^60+1318x^61+653x^62+436x^63+240x^64+144x^65+27x^66+16x^67+4x^68+12x^69+2x^70+1x^72+2x^75+1x^78

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 22.6 seconds.