The generator matrix

 1  0  1  1  1 X+2  1  1  0  1 X+2  1  1  1  0  1 X+2  1  1  1  0  1  1 X+2  1  1  1  1  X  1  2  1  1  1  1  1  1  1 X+2  0  1  1  1  X X+2  0  2  0  1  1  1  X  0  0  1  X  1  2 X+2  1  1  0  1  1
 0  1 X+1 X+2  1  1  0 X+1  1 X+2  1  3 X+1  0  1 X+2  1  3  3  0  1 X+1 X+2  1 X+1  3  3  2  1 X+1  1 X+3 X+2  3 X+1  1  X X+3  1  1  0  1  3 X+2  1  1  1  1 X+2 X+3 X+1  X  1  1 X+1  1  X  X  1 X+3 X+2  X  0  0
 0  0  2  0  0  0  0  0  0  0  0  2  0  2  2  2  2  2  2  2  2  0  2  2  0  0  2  0  2  0  2  2  0  0  0  0  0  0  2  0  2  2  2  2  2  2  0  2  0  0  2  2  2  0  2  2  2  0  0  0  2  0  2  0
 0  0  0  2  0  0  0  2  0  0  2  0  2  2  2  0  2  2  0  2  2  0  2  0  2  0  0  0  0  2  2  0  0  2  0  2  2  0  2  2  0  2  0  2  2  0  2  2  2  2  2  0  0  0  2  0  2  2  2  0  2  2  2  0
 0  0  0  0  2  0  0  0  0  0  0  2  2  0  2  0  2  0  2  2  0  2  2  0  2  0  0  2  2  2  0  2  2  0  0  0  2  2  2  2  0  0  2  0  0  0  2  2  2  0  2  2  2  0  0  0  2  0  0  2  2  2  0  0
 0  0  0  0  0  2  0  2  0  2  0  0  2  0  2  2  2  2  0  2  0  0  2  2  2  2  2  2  0  0  0  2  0  0  2  0  2  2  0  2  2  0  2  0  2  2  0  2  0  2  0  0  2  2  0  0  0  0  0  2  0  0  2  0
 0  0  0  0  0  0  2  2  2  2  2  2  0  0  0  2  2  2  0  0  2  2  2  0  2  2  0  2  0  2  0  0  2  0  0  2  0  0  2  2  0  2  2  2  2  2  0  2  0  0  2  2  0  2  2  0  0  0  0  2  2  0  2  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+48x^57+83x^58+162x^59+99x^60+232x^61+148x^62+210x^63+138x^64+206x^65+137x^66+222x^67+73x^68+142x^69+64x^70+38x^71+4x^72+10x^73+11x^74+8x^75+3x^76+2x^77+2x^78+1x^80+1x^82+1x^84+2x^86

The gray image is a code over GF(2) with n=256, k=11 and d=114.
This code was found by Heurico 1.16 in 0.33 seconds.