The generator matrix

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

generates a code of length 83 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+348x^80+336x^81+364x^82+192x^83+265x^84+160x^85+220x^86+64x^87+51x^88+16x^89+20x^90+1x^92+4x^94+4x^96+1x^108+1x^124

The gray image is a code over GF(2) with n=664, k=11 and d=320.
This code was found by Heurico 1.16 in 0.469 seconds.