The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+30x^61+207x^62+15x^64+2x^77+1x^94

The gray image is a code over GF(2) with n=496, k=8 and d=244.
This code was found by Heurico 1.16 in 13.4 seconds.