The generator matrix

 1  0  0  1  1  1 2X  1  1  1  1  2 2X+2 2X+2  1  1  1 X+2  X  1  1 3X  2  1 3X  1  1  1 3X+2  X 2X+2  1 2X  1 X+2 3X+2  X  0  1  1  X  1 X+2  1  1  1  1  1  X  1  1  1  0  2  0  1  1  1
 0  1  0 2X  3 2X+3  1  X X+3 3X 3X+3  1  X  1 2X+2 2X+1 3X+1  1  0 3X  1  1  1  X X+2  2 2X+3 X+3  1  1 2X+2 2X+2  1 3X+1  1  1  X  1 3X+2 3X+1  1 2X+3  1 X+2 3X+2 3X+2 2X+2  0  1 2X  2  0 3X+2  1 2X+2  X 2X  0
 0  0  1 3X+1 X+1 2X X+1  X 2X+1  1 3X 3X  1 X+1 X+2 2X+3  2 X+2  1 3X+1 3X+2 X+1  1 2X+2  1  3 3X 3X+3 2X+3 2X  1 X+3 2X+3 X+1 2X+2  1  1 2X+2 3X+1 2X+1 3X+3  2 3X+3 2X 2X+3  X 2X+2  X 3X 3X+2  1 X+3  1 2X+3  1  3  3 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+64x^54+522x^55+740x^56+746x^57+561x^58+482x^59+294x^60+246x^61+197x^62+96x^63+51x^64+72x^65+9x^66+12x^67+1x^68+1x^70+1x^76

The gray image is a code over GF(2) with n=464, k=12 and d=216.
This code was found by Heurico 1.16 in 0.187 seconds.