The generator matrix

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

generates a code of length 88 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 83.

Homogenous weight enumerator: w(x)=1x^0+156x^83+433x^84+356x^85+720x^86+286x^87+417x^88+282x^89+518x^90+274x^91+361x^92+158x^93+87x^94+14x^95+18x^96+2x^97+1x^98+4x^99+2x^107+2x^108+2x^109+1x^118+1x^122

The gray image is a code over GF(2) with n=704, k=12 and d=332.
This code was found by Heurico 1.16 in 0.984 seconds.