The generator matrix

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

generates a code of length 77 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+129x^70+670x^71+1535x^72+2190x^73+2980x^74+3314x^75+3892x^76+3994x^77+3836x^78+3186x^79+2749x^80+1764x^81+1253x^82+638x^83+263x^84+190x^85+86x^86+28x^87+29x^88+14x^89+11x^90+4x^91+3x^92+8x^93+1x^94

The gray image is a code over GF(2) with n=616, k=15 and d=280.
This code was found by Heurico 1.16 in 13 seconds.