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

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

Homogenous weight enumerator: w(x)=1x^0+34x^62+16x^63+5x^64+6x^66+2x^68

The gray image is a code over GF(2) with n=496, k=6 and d=248.
This code was found by Heurico 1.16 in 0.14 seconds.