The generator matrix

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

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+178x^53+216x^54+342x^55+567x^56+418x^57+810x^58+448x^59+498x^60+206x^61+142x^62+104x^63+50x^64+62x^65+15x^66+32x^67+4x^68+2x^71+1x^90

The gray image is a code over GF(2) with n=464, k=12 and d=212.
This code was found by Heurico 1.16 in 0.453 seconds.