The generator matrix

 1  0  1  1  1 3X+2  1  1  0  1 3X+2  1  1  1  1 2X  1 3X  1  1  0  1  1 3X  1  1  1 X+2  1  2  1  1  1  2  1  1 3X+2  1  1 X+2  X  1  1  2  1  1  1  1 2X+2  1  X  1 3X  1  1  1  2  1  1  0  1  1  2  2  1  1  1  X  0  1  1  1  1 2X  1  2  1
 0  1 X+1 3X+2  3  1 2X+3  0  1 3X+2  1 X+1 2X+1 X+3 2X  1 3X  1 3X+3  0  1  1 3X  1 3X+3 2X+3  2  1 X+2  1 X+1 3X+2  3  1 3X+3  2  1 2X+1  X  1  1  1  2  1 X+1 2X+2 3X+1 2X+3  1  X  2  1  1 2X+3 3X+3 X+2  X 2X+3  3  1  0  0  1  1 2X 2X+1 3X+3 3X  1  3 X+3  1 2X  X 2X+1  2 X+1
 0  0  2  0  0  0  0  2 2X+2 2X+2  2 2X+2 2X  2 2X+2  2 2X 2X  2 2X 2X 2X  2 2X+2 2X+2  2  0  2  2 2X  0  0 2X+2 2X+2  0 2X+2 2X 2X+2 2X  2  0  2 2X  0 2X  2 2X  2  2 2X+2 2X  0 2X+2  0 2X+2  0  0 2X+2 2X 2X+2  2 2X 2X  0 2X+2  0 2X+2 2X  2  0 2X  2 2X  2  0  0  0
 0  0  0 2X+2 2X 2X+2  2  2 2X+2 2X  0 2X+2  0 2X  0 2X 2X 2X 2X+2 2X+2 2X+2  2  2 2X+2  2  0 2X+2 2X+2 2X+2  2 2X  0 2X+2 2X  2 2X 2X  2 2X+2  2  2 2X 2X  0  0  2  2 2X+2  2  0 2X+2 2X 2X 2X+2 2X+2  2  2  2 2X  2 2X  2 2X 2X 2X 2X+2 2X  2 2X+2  0 2X+2  0  0 2X+2  2  2  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+122x^72+324x^73+480x^74+472x^75+537x^76+490x^77+368x^78+504x^79+323x^80+208x^81+133x^82+28x^83+71x^84+14x^85+8x^86+4x^87+2x^89+1x^90+2x^92+2x^102+2x^105

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 0.594 seconds.