The generator matrix

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

generates a code of length 62 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 59.

Homogenous weight enumerator: w(x)=1x^0+358x^59+300x^60+368x^61+177x^62+222x^63+218x^64+316x^65+28x^66+36x^67+8x^68+8x^69+1x^70+4x^71+1x^78+1x^82+1x^84

The gray image is a code over GF(2) with n=496, k=11 and d=236.
This code was found by Heurico 1.16 in 0.172 seconds.