The generator matrix

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

generates a code of length 62 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+80x^57+285x^58+356x^59+542x^60+476x^61+705x^62+454x^63+490x^64+344x^65+233x^66+68x^67+35x^68+10x^69+6x^70+2x^71+3x^72+2x^77+2x^78+1x^84+1x^94

The gray image is a code over GF(2) with n=496, k=12 and d=228.
This code was found by Heurico 1.16 in 0.344 seconds.