The generator matrix

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

generates a code of length 64 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 61.

Homogenous weight enumerator: w(x)=1x^0+52x^61+164x^62+68x^63+53x^64+20x^65+72x^66+44x^67+2x^68+6x^70+4x^71+8x^72+14x^74+4x^75

The gray image is a code over GF(2) with n=256, k=9 and d=122.
This code was found by Heurico 1.13 in 0.062 seconds.