The generator matrix

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

generates a code of length 93 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 85.

Homogenous weight enumerator: w(x)=1x^0+684x^85+2137x^86+4040x^87+5891x^88+8468x^89+10604x^90+12948x^91+13646x^92+14582x^93+14429x^94+12666x^95+10386x^96+8242x^97+5313x^98+3430x^99+1875x^100+1028x^101+376x^102+146x^103+82x^104+48x^105+15x^106+14x^107+7x^108+2x^109+6x^110+4x^111+2x^113

The gray image is a code over GF(2) with n=744, k=17 and d=340.
This code was found by Heurico 1.16 in 747 seconds.