The generator matrix

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

generates a code of length 64 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 56.

Homogenous weight enumerator: w(x)=1x^0+250x^56+348x^57+864x^58+700x^59+1487x^60+912x^61+1734x^62+1144x^63+1839x^64+1080x^65+1626x^66+996x^67+1274x^68+596x^69+724x^70+288x^71+291x^72+68x^73+100x^74+8x^75+39x^76+4x^77+6x^78+2x^80+2x^82+1x^88

The gray image is a code over GF(2) with n=256, k=14 and d=112.
This code was found by Heurico 1.16 in 11.3 seconds.