The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+530x^54+832x^55+1428x^56+1024x^57+1286x^58+800x^59+991x^60+376x^61+440x^62+248x^63+128x^64+40x^65+46x^66+8x^67+9x^68+2x^70+3x^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 1.2 seconds.