The generator matrix

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

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+159x^58+246x^59+458x^60+452x^61+358x^62+384x^63+352x^64+296x^65+355x^66+254x^67+220x^68+134x^69+163x^70+92x^71+61x^72+44x^73+42x^74+16x^75+4x^76+2x^77+3x^78

The gray image is a code over GF(2) with n=256, k=12 and d=116.
This code was found by Heurico 1.16 in 0.669 seconds.