The generator matrix

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

generates a code of length 64 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 57.

Homogenous weight enumerator: w(x)=1x^0+76x^57+182x^58+280x^59+297x^60+334x^61+397x^62+338x^63+379x^64+424x^65+368x^66+294x^67+230x^68+168x^69+122x^70+88x^71+35x^72+14x^73+13x^74+22x^75+12x^76+6x^77+4x^78+2x^79+5x^80+2x^81+1x^82+1x^84+1x^86

The gray image is a code over GF(2) with n=256, k=12 and d=114.
This code was found by Heurico 1.16 in 1.02 seconds.