The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+114x^58+5x^60+4x^62+1x^64+2x^66+1x^68

The gray image is a code over GF(2) with n=464, k=7 and d=232.
This code was found by Heurico 1.16 in 0.093 seconds.