The generator matrix

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

generates a code of length 58 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+116x^54+222x^55+153x^56+436x^57+232x^58+400x^59+155x^60+204x^61+98x^62+18x^63+10x^64+1x^70+1x^84+1x^86

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 0.141 seconds.