The generator matrix

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

generates a code of length 58 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+32x^52+54x^53+61x^54+80x^55+119x^56+404x^57+654x^58+370x^59+74x^60+60x^61+34x^62+28x^63+17x^64+22x^65+13x^66+2x^67+10x^68+2x^69+5x^70+3x^72+2x^73+1x^98

The gray image is a code over GF(2) with n=464, k=11 and d=208.
This code was found by Heurico 1.16 in 0.25 seconds.