The generator matrix

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

generates a code of length 83 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+128x^77+792x^78+1390x^79+1526x^80+2134x^81+1738x^82+2070x^83+1617x^84+1448x^85+1172x^86+958x^87+529x^88+402x^89+159x^90+150x^91+102x^92+16x^93+25x^94+8x^95+14x^96+3x^100+1x^102+1x^106

The gray image is a code over GF(2) with n=664, k=14 and d=308.
This code was found by Heurico 1.16 in 3.81 seconds.