The generator matrix

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

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+130x^71+105x^72+336x^73+240x^74+520x^75+433x^76+656x^77+450x^78+496x^79+211x^80+252x^81+44x^82+128x^83+39x^84+24x^85+2x^86+6x^87+10x^88+12x^89+1x^128

The gray image is a code over GF(2) with n=616, k=12 and d=284.
This code was found by Heurico 1.16 in 1.25 seconds.