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

generates a code of length 79 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+132x^76+352x^78+468x^80+32x^82+36x^84+2x^88+1x^144

The gray image is a code over GF(2) with n=632, k=10 and d=304.
This code was found by Heurico 1.16 in 4.16 seconds.