The generator matrix

 1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  4  0  2  1  4  2  2  4  2  2  0  0  1  1  0  0  1  2  2  0
 0  2  0  0  0  0  0  0  0  0  0  4  2  6  2  4  2  0  2  6  2  2  6  0  4  2  4  6  6  2  6  0  4  0  0  2  4  4  0  4  0  6  2  2  2  2  6  0  2  2  2  2  4  0  4  2  6  0  2  2  0  6  4  2
 0  0  2  0  0  0  0  0  0  0  0  6  4  2  2  2  2  2  6  0  4  4  2  6  0  2  2  6  0  6  2  6  4  2  6  4  6  6  4  2  2  2  2  0  4  0  6  0  2  6  0  4  4  4  2  2  2  4  2  0  2  0  4  2
 0  0  0  2  0  0  0  2  6  2  4  2  6  4  2  2  0  0  6  4  2  6  4  4  4  6  0  6  0  0  2  4  2  2  6  4  0  4  0  6  2  6  0  4  0  0  2  6  4  2  6  0  4  6  6  0  0  2  0  0  2  6  4  0
 0  0  0  0  2  0  2  2  2  4  6  0  4  2  6  4  6  4  6  2  6  2  4  6  0  0  0  4  6  4  4  2  2  6  2  0  2  2  0  4  6  4  6  6  6  4  6  6  6  6  0  2  2  4  6  2  0  4  6  6  0  4  2  2
 0  0  0  0  0  2  2  4  6  2  0  0  0  4  4  6  6  6  2  2  2  0  6  0  4  0  6  2  6  0  2  4  2  0  2  2  6  2  6  4  2  4  4  0  0  4  2  4  6  4  4  0  0  6  0  6  2  2  6  2  0  2  4  4
 0  0  0  0  0  0  4  4  4  0  4  0  0  4  4  4  0  4  0  0  0  4  4  4  4  4  0  0  4  0  4  0  0  4  4  0  0  4  4  4  0  0  0  0  0  4  0  0  4  0  0  4  0  0  4  4  4  4  4  4  4  4  4  4

generates a code of length 64 over Z8 who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+76x^53+173x^54+264x^55+329x^56+446x^57+512x^58+686x^59+912x^60+972x^61+1371x^62+1640x^63+1623x^64+1668x^65+1390x^66+1060x^67+926x^68+684x^69+481x^70+328x^71+237x^72+214x^73+154x^74+110x^75+58x^76+28x^77+15x^78+8x^79+9x^80+8x^81+1x^96

The gray image is a code over GF(2) with n=256, k=14 and d=106.
This code was found by Heurico 1.16 in 16.2 seconds.