The generator matrix

 1  0  0  1  1  1  2  0  1  1  2 X^2  1  1  1  1 X+2  1  1 X^2+X+2  1 X+2 X+2  1  1  1 X^2+X+2 X^2  1  2 X^2+X+2  1  1  1  1  1 X^2+X+2  1 X^2+X+2  1 X^2+2 X^2+X+2  1  1  2  1  1  1  1 X^2+X  1  1  1  0 X^2+2 X^2+X+2 X^2+2 X^2+2 X^2+X X^2+X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  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^2+X X+3  1 X+3  0  1 X^2+X+2 X+1  X X+2  1  2  1 X^2+X X^2+X+1 X^2+2 X^2+X X^2+3 X^2+X  1 X^2+X+3 X^2  1 X^2  1 X+1 X^2+3 X^2+X+2 X+1 X+2  0  3  1  1 X^2+2  X  X  1  1  1  2  1  2 X^2+X+1 X^2+X+2 X^2+X+3  3  X X^2+2 X^2+X+3  3 X+1 X^2+X+2 X^2+2  1  3 X^2+X+3 X+3 X^2  2 X^2+X X^2+X+2 X+2 X^2+X+1  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 X^2+X  1 X^2  X  1  X  2 X^2+X+3 X+1  1 X+1 X^2+X+1 X^2+3  1 X+2 X^2+2 X^2+1 X^2+X+1 X^2+2 X^2+X+1 X^2  1 X^2  1 X^2+1 X+3 X^2+3  1 X^2+3  1  3 X+2 X^2+X+1 X+3  X X^2+X  1 X^2+X+2 X^2+2 X^2  1  X  1 X^2+X+2 X^2+X+1 X^2+X+3  1 X^2+X+3 X^2 X+1  3 X^2+3  1  0 X^2+X+1 X+3 X^2+1  1 X+1 X^2+1 X^2+X+3  3 X^2+2  1  0
 0  0  0  2  2  0  2  2  2  0  0  2  0  2  0  2  2  0  2  2  0  0  0  2  0  2  2  0  0  2  0  2  2  2  2  0  0  0  0  2  2  0  2  2  0  0  0  2  0  2  0  0  2  2  0  0  2  2  2  2  0  2  0  2  0  0  0  0  2  2  2  0  2  0  0  0  2  0  0  0  2  0

generates a code of length 82 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+204x^77+789x^78+904x^79+1063x^80+1142x^81+917x^82+846x^83+603x^84+550x^85+376x^86+210x^87+352x^88+132x^89+44x^90+40x^91+12x^92+4x^93+1x^100+1x^106+1x^110

The gray image is a code over GF(2) with n=656, k=13 and d=308.
This code was found by Heurico 1.16 in 1.09 seconds.