The generator matrix

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

generates a code of length 77 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+210x^68+1282x^69+3071x^70+5526x^71+9872x^72+14264x^73+21605x^74+25806x^75+33002x^76+32126x^77+33276x^78+26676x^79+21729x^80+14654x^81+9862x^82+4790x^83+2467x^84+1100x^85+475x^86+178x^87+72x^88+42x^89+26x^90+16x^91+7x^92+4x^93+4x^94+1x^98

The gray image is a code over GF(2) with n=616, k=18 and d=272.
This code was found by Heurico 1.16 in 686 seconds.