The generator matrix

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

generates a code of length 77 over Z4[X]/(X^3+2,2X) 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 0.579 seconds.