The generator matrix

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

generates a code of length 89 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+576x^80+1852x^81+3886x^82+6372x^83+11451x^84+15184x^85+21298x^86+25240x^87+30010x^88+30088x^89+30604x^90+25884x^91+21529x^92+14884x^93+10742x^94+5988x^95+3551x^96+1532x^97+720x^98+416x^99+226x^100+36x^101+40x^102+4x^103+13x^104+8x^105+2x^106+2x^108+2x^110+1x^112+2x^118

The gray image is a code over GF(2) with n=712, k=18 and d=320.
This code was found by Heurico 1.16 in 808 seconds.