The generator matrix

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

generates a code of length 64 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 58.

Homogenous weight enumerator: w(x)=1x^0+144x^58+244x^59+541x^60+256x^61+486x^62+372x^63+486x^64+232x^65+330x^66+192x^67+243x^68+120x^69+170x^70+76x^71+99x^72+32x^73+54x^74+12x^75+4x^76+2x^80

The gray image is a code over GF(2) with n=256, k=12 and d=116.
This code was found by Heurico 1.11 in 0.352 seconds.