The generator matrix

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

generates a code of length 64 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 54.

Homogenous weight enumerator: w(x)=1x^0+62x^54+136x^55+238x^56+444x^57+605x^58+736x^59+930x^60+1220x^61+1412x^62+1576x^63+1700x^64+1658x^65+1512x^66+1154x^67+911x^68+698x^69+454x^70+376x^71+238x^72+114x^73+71x^74+44x^75+39x^76+26x^77+12x^78+8x^79+6x^80+2x^83+1x^88

The gray image is a code over GF(2) with n=256, k=14 and d=108.
This code was found by Heurico 1.16 in 14.3 seconds.