The generator matrix

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

generates a code of length 61 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+16x^62+8x^63+5x^64+2x^68

The gray image is a code over GF(2) with n=488, k=5 and d=248.
This code was found by Heurico 1.16 in 0.109 seconds.