The generator matrix

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

generates a code of length 61 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+212x^57+458x^58+764x^59+463x^60+698x^61+462x^62+366x^63+207x^64+194x^65+94x^66+102x^67+32x^68+32x^69+8x^70+1x^74+1x^76+1x^82

The gray image is a code over GF(2) with n=488, k=12 and d=228.
This code was found by Heurico 1.16 in 0.359 seconds.