The generator matrix

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

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+214x^83+235x^84+508x^85+494x^86+550x^87+363x^88+420x^89+494x^90+326x^91+163x^92+164x^93+27x^94+90x^95+3x^96+28x^97+6x^98+4x^99+2x^100+2x^102+1x^126+1x^128

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 1.09 seconds.