The generator matrix

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

generates a code of length 77 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+258x^69+1486x^70+2876x^71+5501x^72+7764x^73+10884x^74+12548x^75+15628x^76+16050x^77+17097x^78+13510x^79+11098x^80+6718x^81+4832x^82+2434x^83+1273x^84+666x^85+251x^86+102x^87+32x^88+42x^89+10x^90+2x^91+6x^93+2x^96+1x^100

The gray image is a code over GF(2) with n=616, k=17 and d=276.
This code was found by Heurico 1.16 in 163 seconds.