The generator matrix

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

generates a code of length 88 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+571x^80+1978x^81+3854x^82+5690x^83+7883x^84+10566x^85+12753x^86+14406x^87+15422x^88+15128x^89+13650x^90+9996x^91+7615x^92+5308x^93+2999x^94+1688x^95+768x^96+422x^97+226x^98+82x^99+28x^100+6x^101+20x^102+10x^103+2x^110

The gray image is a code over GF(2) with n=704, k=17 and d=320.
This code was found by Heurico 1.16 in 226 seconds.