The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+148x^68+1254x^69+2891x^70+6324x^71+9219x^72+14974x^73+19909x^74+27438x^75+30401x^76+35480x^77+31567x^78+28870x^79+20346x^80+15144x^81+8215x^82+5042x^83+2736x^84+1320x^85+378x^86+286x^87+116x^88+48x^89+16x^90+8x^91+6x^92+2x^93+2x^96+2x^97+1x^100

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 720 seconds.