The generator matrix

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

generates a code of length 88 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+604x^81+1852x^82+3318x^83+4622x^84+5550x^85+6400x^86+7526x^87+7107x^88+7254x^89+6216x^90+5190x^91+3849x^92+2722x^93+1644x^94+838x^95+470x^96+206x^97+68x^98+52x^99+13x^100+16x^101+12x^102+4x^103+2x^104

The gray image is a code over GF(2) with n=704, k=16 and d=324.
This code was found by Heurico 1.16 in 53.1 seconds.