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

generates a code of length 77 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+23x^74+74x^76+320x^77+68x^78+20x^80+3x^82+1x^88+2x^110

The gray image is a code over GF(2) with n=616, k=9 and d=296.
This code was found by Heurico 1.16 in 0.469 seconds.