The generator matrix

 1  0  0  0  1  1  1  1  2  1 X+2  1  X X+2  1  1  1  2  0 X+2  0  1  1  X  1  2  1  1  1  0  1  1  1  1  2 X+2  1  2  1 X+2 X+2  0  2  1  X  1  1 X+2  X  1  1 X+2  X  1  X  X  1  0  1  1  1 X+2  0  1
 0  1  0  0  0  2  1  3  1  2  0  3  1  1 X+1 X+2 X+2  1  1  0  1  0 X+2  X  3 X+2 X+1  1 X+3  1 X+2  3  2  2  1 X+2 X+1  1  1  0  1  1  1  0  1  3 X+1  1  1  1 X+2  X  2  3  X  1  2  1 X+1  2 X+1 X+2  1  1
 0  0  1  0  0  3  1  2  3  1  1 X+1  3  X  X  2 X+3 X+1  1  2  2 X+2 X+3  1  1  1  X X+1 X+2  2  3  3 X+1  X  1  1 X+3 X+1  2  1 X+2 X+2  2 X+3  0  2  1  1  1 X+2  0  1  1  3  2 X+2  2  X  3 X+1  2  1  1 X+2
 0  0  0  1  1  1  2  3  3  0 X+1 X+1  2  1 X+2 X+3  3  0 X+1  1 X+2 X+2  2  X  X  3  1 X+1 X+2 X+1 X+3  0  X  2  2  X  0 X+3  0 X+3 X+3  3  X X+3  3  0  X X+2 X+1  1  3 X+1  X X+3  1  X X+3  0  0  0 X+3 X+1  3  3
 0  0  0  0  X  0  0  0  0  2  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2 X+2  X  X X+2 X+2  X X+2  X X+2  X X+2  X X+2 X+2  X  2  X X+2  2 X+2  2  0 X+2  X  2 X+2  X  X  2  X X+2  X  2  2  X  2  0 X+2  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+180x^56+442x^57+782x^58+932x^59+1225x^60+1176x^61+1387x^62+1344x^63+1637x^64+1420x^65+1469x^66+1108x^67+1018x^68+714x^69+711x^70+376x^71+210x^72+110x^73+59x^74+42x^75+17x^76+10x^77+6x^78+4x^79+2x^82+2x^83

The gray image is a code over GF(2) with n=256, k=14 and d=112.
This code was found by Heurico 1.13 in 4.33 seconds.