The generator matrix

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

generates a code of length 58 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 55.

Homogenous weight enumerator: w(x)=1x^0+292x^55+367x^56+344x^57+189x^58+292x^59+243x^60+202x^61+57x^62+36x^63+4x^64+10x^65+1x^66+8x^67+1x^80+1x^82

The gray image is a code over GF(2) with n=464, k=11 and d=220.
This code was found by Heurico 1.16 in 0.156 seconds.