The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+142x^81+923x^82+1556x^83+2406x^84+2958x^85+3439x^86+3686x^87+3592x^88+3524x^89+3078x^90+2414x^91+2106x^92+1354x^93+779x^94+388x^95+229x^96+66x^97+38x^98+18x^99+24x^100+20x^101+14x^102+2x^103+10x^104+1x^106

The gray image is a code over GF(2) with n=704, k=15 and d=324.
This code was found by Heurico 1.16 in 15.6 seconds.