The generator matrix

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

generates a code of length 85 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+377x^76+1682x^77+3546x^78+6218x^79+11065x^80+15078x^81+20879x^82+26318x^83+30224x^84+30670x^85+31194x^86+26276x^87+21827x^88+15158x^89+10154x^90+5728x^91+3046x^92+1542x^93+640x^94+260x^95+135x^96+56x^97+19x^98+30x^99+9x^100+6x^101+2x^103+2x^104+2x^112

The gray image is a code over GF(2) with n=680, k=18 and d=304.
This code was found by Heurico 1.16 in 724 seconds.