The generator matrix

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

generates a code of length 83 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+180x^78+616x^79+1035x^80+1200x^81+1078x^82+1024x^83+848x^84+536x^85+484x^86+412x^87+309x^88+208x^89+78x^90+56x^91+78x^92+40x^93+1x^94+4x^95+1x^96+2x^98+1x^102

The gray image is a code over GF(2) with n=664, k=13 and d=312.
This code was found by Heurico 1.16 in 1.14 seconds.