The generator matrix

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

generates a code of length 64 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+222x^54+614x^55+1063x^56+1656x^57+2308x^58+3324x^59+3757x^60+5004x^61+5303x^62+6172x^63+6068x^64+6574x^65+5742x^66+5088x^67+3989x^68+3170x^69+2184x^70+1484x^71+754x^72+516x^73+290x^74+144x^75+46x^76+38x^77+15x^78+6x^79+2x^80+2x^81

The gray image is a code over GF(2) with n=256, k=16 and d=108.
This code was found by Heurico 1.13 in 59.1 seconds.