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

generates a code of length 81 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+32x^77+16x^78+126x^80+704x^81+96x^82+32x^85+16x^86+1x^160

The gray image is a code over GF(2) with n=648, k=10 and d=308.
This code was found by Heurico 1.16 in 0.953 seconds.