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

generates a code of length 68 over Z4[X]/(X^2+2) who�s minimum homogenous weight is 64.

Homogenous weight enumerator: w(x)=1x^0+108x^64+300x^65+416x^66+304x^67+100x^68+172x^69+292x^70+160x^71+38x^72+52x^73+24x^74+16x^75+24x^76+20x^77+20x^78+1x^128

The gray image is a code over GF(2) with n=544, k=11 and d=256.
This code was found by Heurico 1.16 in 0.578 seconds.