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

generates a code of length 64 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 53.

Homogenous weight enumerator: w(x)=1x^0+82x^53+181x^54+234x^55+362x^56+422x^57+485x^58+606x^59+899x^60+1100x^61+1386x^62+1616x^63+1627x^64+1702x^65+1362x^66+1184x^67+866x^68+578x^69+517x^70+342x^71+286x^72+178x^73+139x^74+98x^75+51x^76+32x^77+20x^78+16x^79+4x^80+2x^81+5x^82+1x^98

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 29.4 seconds.