The generator matrix

 1  0  0  1  1  1  2  0  1  1  2 X^2  1  1  1  1 X+2 X^2+X X^2+X+2  1  1 X^2+X  1  1 X^2+X+2  1 X^2+X  1 X^2+2  1 X^2  1 X+2  1  1 X^2+X  1 X^2+2  1  1 X^2+X+2  1  1  1  2  2  1 X^2+X+2 X^2+2  1 X^2+X X^2+X  1  1  1 X^2  X  1  1 X^2+2  1  1  1  1  1  1  1  1  1  1 X^2+X X+2  1  1  2  1  1
 0  1  0  0 X^2+1 X^2+1  1 X^2+X  2 X^2+3  1  1 X^2+2  3 X^2+X+2 X+1  1  X  1 X^2+X+3 X^2+X X^2  X X+3  1 X+3  1 X+2  2 X+3  1 X^2+2  X  2 X^2+X+2  1 X^2+X+1  1 X^2+3  0  1  X  1  1 X^2+X+2  1 X^2+2  0  1 X^2+X+3  1  1 X^2+X+1 X^2+X+3  X  1  1  1  X X^2+2 X^2+X+3  2 X+2  3 X^2+1 X^2 X^2+X X^2+2  0 X^2+X+1  1  0 X^2+3 X^2+3 X^2  X  0
 0  0  1 X+1 X+3  2 X^2+X+3  1 X^2+X+2 X^2+1  1 X+2 X^2+3  X X+3 X^2 X^2+3  1 X^2+X X^2+X+1 X^2+2  1 X^2+3  1 X^2  X X+3 X^2+X  1 X+3 X^2+X+3  2  1 X+1  2 X+2  3  X  3 X^2+X+3  1 X+1 X^2+2 X^2+X+1  1 X^2+3  3  1 X^2 X^2+X+1 X^2+1 X^2+X+3 X^2 X^2+1  X X^2+3 X^2+2  2 X^2+3  1 X+3 X^2+X X^2+X+3  0 X^2+X+3 X^2+1  1 X+1 X^2+1  X  0  1 X^2+X+2 X^2+X+2  1  1  0
 0  0  0  2  2  0  2  2  2  0  0  2  0  2  0  2  2  2  2  0  0  0  2  2  2  0  2  0  2  2  0  2  0  0  2  0  0  0  2  2  0  2  2  0  0  2  2  2  2  2  0  0  0  2  2  2  0  0  0  2  0  0  0  2  2  2  2  0  0  2  0  0  0  2  2  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+135x^72+736x^73+933x^74+1238x^75+970x^76+1052x^77+822x^78+644x^79+471x^80+476x^81+255x^82+238x^83+69x^84+84x^85+53x^86+8x^87+4x^89+1x^92+1x^94+1x^96

The gray image is a code over GF(2) with n=616, k=13 and d=288.
This code was found by Heurico 1.16 in 0.969 seconds.