The generator matrix

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

generates a code of length 77 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+135x^72+202x^73+587x^74+534x^75+650x^76+248x^77+536x^78+266x^79+448x^80+236x^81+136x^82+14x^83+40x^84+28x^85+15x^86+2x^87+6x^88+6x^89+2x^90+2x^94+1x^106+1x^110

The gray image is a code over GF(2) with n=616, k=12 and d=288.
This code was found by Heurico 1.16 in 0.703 seconds.