The generator matrix

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

generates a code of length 88 over Z4[X]/(X^2+2X+2) 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.