The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+625x^80+1676x^81+3952x^82+6624x^83+11056x^84+15652x^85+21254x^86+25464x^87+28929x^88+31448x^89+29238x^90+26080x^91+21500x^92+15892x^93+10256x^94+5824x^95+3639x^96+1588x^97+910x^98+224x^99+167x^100+80x^101+40x^102+8x^103+2x^104+12x^106+2x^110+1x^124

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 888 seconds.