The generator matrix

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

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+190x^57+344x^58+584x^59+647x^60+732x^61+676x^62+800x^63+654x^64+666x^65+661x^66+634x^67+440x^68+434x^69+240x^70+190x^71+131x^72+88x^73+29x^74+30x^75+15x^76+2x^77+2x^78+2x^79

The gray image is a code over GF(2) with n=256, k=13 and d=114.
This code was found by Heurico 1.13 in 1.21 seconds.