The generator matrix

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

generates a code of length 58 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+621x^54+744x^55+1288x^56+1128x^57+1398x^58+744x^59+893x^60+504x^61+414x^62+176x^63+174x^64+32x^65+62x^66+11x^68+1x^70+1x^72

The gray image is a code over GF(2) with n=464, k=13 and d=216.
This code was found by Heurico 1.16 in 30.6 seconds.