The generator matrix

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

generates a code of length 64 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 62.

Homogenous weight enumerator: w(x)=1x^0+232x^62+122x^64+112x^66+40x^70+4x^72+1x^96

The gray image is a code over GF(2) with n=256, k=9 and d=124.
This code was found by Heurico 1.16 in 25.1 seconds.