The generator matrix

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

generates a code of length 83 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+100x^76+778x^77+1620x^78+2224x^79+2757x^80+3530x^81+4030x^82+3720x^83+3795x^84+3354x^85+2297x^86+1784x^87+1196x^88+730x^89+455x^90+160x^91+81x^92+76x^93+43x^94+16x^95+5x^96+12x^97+3x^98+1x^104

The gray image is a code over GF(2) with n=664, k=15 and d=304.
This code was found by Heurico 1.16 in 13.1 seconds.