The generator matrix

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

generates a code of length 77 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+90x^71+818x^72+1054x^73+1847x^74+1878x^75+2000x^76+1808x^77+1934x^78+1422x^79+1424x^80+808x^81+644x^82+262x^83+222x^84+84x^85+35x^86+12x^87+29x^88+6x^89+3x^90+1x^94+2x^96

The gray image is a code over GF(2) with n=616, k=14 and d=284.
This code was found by Heurico 1.16 in 3.91 seconds.