The generator matrix

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

generates a code of length 62 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+76x^58+540x^59+780x^60+646x^61+662x^62+444x^63+316x^64+154x^65+143x^66+156x^67+57x^68+52x^69+37x^70+24x^71+6x^72+2x^74

The gray image is a code over GF(2) with n=496, k=12 and d=232.
This code was found by Heurico 1.16 in 0.219 seconds.