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  2  X  X  1  0  2  X  2  1  2  2  0  X  1  2  1  0  1  1  0  1  1  1  2  X  1  1  2  1  2
 0  X  0  0  0  X X+2  X  0  2  2  X X+2  X  X  0  0  0  2 X+2 X+2  2 X+2  X X+2  0  0 X+2  X  0  X  2  X  2  X  X  X  2  0  X  0  X  2  X  2  X  0  0  X  X  X  X X+2  0  0  2  0  X X+2 X+2  0  2  0  2
 0  0  X  0  X  X X+2  0  0  0  X  X  X  0  2 X+2  X  0  2  2  0  0 X+2  2  X X+2  2 X+2  0 X+2  X X+2  X  X  X X+2  0  2  X  2 X+2 X+2  0 X+2  X  2  X  2  2  X  X X+2 X+2  X  2  2  0 X+2 X+2  0 X+2  X X+2  2
 0  0  0  X  X  0 X+2  X  2  X  2  0  X  2 X+2  X  2  2  X X+2  2  X  0  X X+2 X+2  0 X+2  0  0  0 X+2 X+2  2  0  0 X+2  0  0 X+2  0  2  X  0 X+2  0  2  X X+2  0  X  2  0  0  2  2 X+2  0  0  X  0  X  X  2
 0  0  0  0  2  0  0  0  2  2  2  2  2  0  0  2  2  0  2  2  0  2  2  0  0  0  0  2  2  2  2  2  0  0  0  0  2  0  2  0  2  0  0  0  0  2  0  2  2  2  2  0  0  0  0  2  0  2  2  0  0  2  2  0
 0  0  0  0  0  2  0  0  0  2  0  2  2  2  0  0  2  2  2  2  0  0  0  2  0  0  0  0  2  2  0  0  2  2  0  0  2  2  2  2  0  2  2  2  0  2  0  0  0  0  2  0  2  0  2  2  2  2  0  0  0  2  2  0
 0  0  0  0  0  0  2  0  2  0  0  2  2  2  0  0  2  0  2  2  2  0  2  0  0  0  2  0  0  0  2  2  0  2  2  2  2  0  2  2  0  2  0  0  2  0  0  2  2  0  0  0  0  0  2  0  0  2  2  2  2  0  0  2
 0  0  0  0  0  0  0  2  0  0  2  0  0  0  0  2  0  0  0  2  2  2  2  2  2  2  0  2  2  0  0  2  2  0  2  0  0  2  2  0  2  2  0  2  2  2  0  0  0  0  2  0  2  2  0  2  2  0  0  0  0  2  2  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+124x^54+12x^55+351x^56+44x^57+468x^58+148x^59+746x^60+384x^61+947x^62+460x^63+1022x^64+388x^65+934x^66+380x^67+622x^68+204x^69+422x^70+24x^71+257x^72+140x^74+63x^76+4x^77+35x^78+9x^80+2x^82+1x^92

The gray image is a code over GF(2) with n=256, k=13 and d=108.
This code was found by Heurico 1.16 in 5.58 seconds.