The generator matrix

 1  0  1  1  1 X+2  1  1  2  1  1 2X  1  1  X  1  1  1  1  X  1  1 2X+2 3X+2  2 3X 2X 3X+2 2X  X X+2 2X  1  1  1  1  1  1  1  1  1 2X 3X+2  1  1 2X+2  1 2X+2  1  1  1  1  1  1 X+2  X  X  1
 0  1 X+1 X+2 2X+3  1 2X 3X+3  1  2 X+1  1  X 2X+1  1 2X+2  3 3X+2 X+3  1 3X  1  1  1  1  1  1  1  1  1  1  1  0 3X+2 3X+2  0  2  X  0  2  X  X  1  2 3X  1 2X+1  1  2 2X+2 3X+2 X+1  X 3X  1  X 3X  0
 0  0 2X+2 2X+2 2X 2X+2  2  2 2X 2X  0  2 2X+2 2X 2X+2  2 2X+2  0  0 2X+2 2X  2  2  0  0 2X 2X+2 2X 2X  0  2  2 2X  0 2X+2 2X+2  0  2  0  2  0 2X  2 2X+2 2X 2X  0 2X+2 2X+2 2X 2X 2X 2X+2  2  0 2X+2  2 2X
 0  0  0 2X  0  0  0 2X 2X 2X 2X 2X  0 2X 2X 2X 2X 2X  0  0  0  0 2X  0 2X  0  0 2X  0 2X 2X  0 2X  0  0 2X  0 2X 2X  0 2X 2X  0  0 2X  0  0  0 2X  0  0  0 2X  0 2X  0 2X 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+59x^54+356x^55+224x^56+294x^57+227x^58+296x^59+172x^60+308x^61+80x^62+20x^63+1x^64+6x^65+1x^70+2x^72+1x^90

The gray image is a code over GF(2) with n=464, k=11 and d=216.
This code was found by Heurico 1.16 in 0.204 seconds.