The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+660x^81+1836x^82+3352x^83+4204x^84+6054x^85+6297x^86+7498x^87+6985x^88+7222x^89+6186x^90+5476x^91+3822x^92+2802x^93+1361x^94+984x^95+420x^96+186x^97+84x^98+60x^99+16x^100+12x^102+6x^103+8x^104+4x^105

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 50.3 seconds.