The generator matrix

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

generates a code of length 64 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 52.

Homogenous weight enumerator: w(x)=1x^0+55x^52+216x^53+734x^54+1344x^55+2022x^56+3260x^57+4237x^58+6270x^59+7524x^60+9758x^61+10471x^62+12864x^63+12628x^64+13126x^65+11474x^66+9914x^67+7653x^68+6166x^69+4234x^70+3048x^71+1703x^72+1166x^73+533x^74+334x^75+171x^76+100x^77+29x^78+16x^79+14x^80+2x^83+5x^84

The gray image is a code over GF(2) with n=256, k=17 and d=104.
This code was found by Heurico 1.13 in 367 seconds.