The generator matrix

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

generates a code of length 89 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+609x^80+1684x^81+3996x^82+6636x^83+11514x^84+15332x^85+20746x^86+25240x^87+29403x^88+30296x^89+30656x^90+26520x^91+21668x^92+14932x^93+10584x^94+5880x^95+3338x^96+1552x^97+858x^98+348x^99+193x^100+72x^101+34x^102+16x^103+21x^104+4x^105+6x^106+4x^108+1x^116

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 772 seconds.