The generator matrix

 1  0  0  1  1  1 2X  1  1  0  1  1  2 3X  1 3X+2  1 2X X+2  1  1 X+2  1  1  1 3X+2  1  2  X  1 X+2  1 2X  1  1  1  1  1  1 X+2  2 3X+2  1  1 3X  2  1 3X+2  2  1  0 2X  1  2  X  1  1  1  1  1  0  X X+2  2  0  1  1  1
 0  1  0 2X  3 2X+3  1  X 3X 3X X+3 3X+3  1  1  0  1 X+3  1 2X+2 3X 3X+3  1 2X 3X+2 3X+1 3X  3  1  1 X+2 3X+2 3X+3 2X+2 2X+3  0  2 2X+1 2X+2 3X+2  1  0  1 2X+2  1  1  1  X  1  1 X+1  1  1  2  1  1 3X+2  X X+1  2  3 3X+2 3X  1 X+2  1  1 2X+1  0
 0  0  1 3X+1 X+1 2X X+1  X  3  1 2X+3 3X X+2 2X+3 3X+2  0 X+3 2X+3  1 3X+1 2X 3X+1  1  2 X+2  1 2X+3  X 2X+2  0  1  2  1  X  X 2X+2 2X+1  1 X+2 3X+3  1 3X+2 3X+3 X+1  X 2X+3 2X+1  3 X+3 2X  2 X+2  X 3X+1  1 3X 2X  3  0  2  1  1  1  1 3X 3X+2 2X+3  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+140x^64+590x^65+694x^66+764x^67+356x^68+526x^69+314x^70+224x^71+126x^72+144x^73+85x^74+88x^75+41x^76+2x^82+1x^86

The gray image is a code over GF(2) with n=544, k=12 and d=256.
This code was found by Heurico 1.16 in 0.266 seconds.