The generator matrix

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

generates a code of length 88 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 79.

Homogenous weight enumerator: w(x)=1x^0+456x^79+1748x^80+4038x^81+6430x^82+11592x^83+14747x^84+21128x^85+24963x^86+30690x^87+29652x^88+31514x^89+25471x^90+22540x^91+14484x^92+10256x^93+5917x^94+3508x^95+1670x^96+772x^97+275x^98+164x^99+57x^100+32x^101+12x^102+6x^103+8x^104+4x^106+2x^107+4x^109+1x^112+2x^115

The gray image is a code over GF(2) with n=704, k=18 and d=316.
This code was found by Heurico 1.16 in 802 seconds.