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

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+88x^54+373x^56+36x^57+601x^58+152x^59+711x^60+320x^61+885x^62+488x^63+979x^64+536x^65+877x^66+360x^67+646x^68+128x^69+443x^70+24x^71+285x^72+4x^73+148x^74+70x^76+28x^78+5x^80+2x^82+1x^84+1x^88

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 5.55 seconds.