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  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  X  X  X  X  2  2  X  X X^2 X^2  X  X X^2
 0  X  0  X  0  2 X+2  X X^2 X^2+X X^2 X^2+X+2 X^2 X^2+2 X^2+X+2 X^2+X+2  0 X^2+2  X X^2+X+2  X  0  2 X+2 X^2  0 X^2+X X+2 X^2 X^2+X+2 X^2+X  0 X^2  X X+2  0  2  X  0  X X^2+X+2 X^2 X^2+2  2  X X^2+X+2  2 X+2 X^2 X^2+2 X^2+X X^2+X+2 X^2+2 X^2 X^2+X+2 X^2+X X^2+2 X^2  0  2 X^2+X X^2+X+2 X+2  X X^2 X^2+2  X  X  X  X X^2+X X^2+X  X  X X^2 X^2+2  2
 0  0  X  X X^2+2 X^2+X+2 X^2+X X^2 X^2 X^2+X+2  X  0  2 X^2+X+2 X+2 X^2  0 X+2  X X^2 X^2+X+2  X X^2+2 X^2+2 X^2 X^2+X X^2+X+2  2 X^2+X X+2  2  2  2 X+2 X^2  X X^2 X^2 X+2 X^2+X+2 X^2+2  X  X  2 X^2+X X^2 X^2 X+2 X^2+2 X^2+2 X^2+X+2 X^2+X+2  2  2  X  X X^2+X X^2+X X^2+X+2 X^2+X+2  0  0  2  2  X X+2  X X+2 X^2 X^2+2  0  2  X X+2  X X^2+X  2
 0  0  0  2  0  0  2  0  2  0  2  2  2  2  0  2  0  2  0  2  0  0  2  0  0  2  2  2  0  2  0  2  0  2  2  2  0  2  2  0  0  0  0  2  2  0  2  0  2  0  0  2  2  0  2  0  2  0  0  2  2  0  2  0  0  0  0  0  0  0  2  2  0  0  2  2  0
 0  0  0  0  2  2  2  2  2  2  0  0  0  2  0  2  2  2  0  0  2  2  2  0  0  0  0  2  0  2  2  0  2  2  2  2  0  0  0  0  2  2  0  2  0  0  0  2  0  2  0  2  2  0  0  2  0  2  0  2  2  0  0  2  0  0  0  0  2  2  2  2  2  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+510x^72+64x^73+416x^74+256x^75+624x^76+384x^77+512x^78+256x^79+606x^80+64x^81+352x^82+48x^84+2x^88+1x^128

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 0.812 seconds.