The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+60x^61+160x^62+31x^64+4x^77

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 6.67 seconds.