The generator matrix

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

generates a code of length 83 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 74.

Homogenous weight enumerator: w(x)=1x^0+310x^74+1454x^75+3623x^76+6312x^77+10134x^78+15414x^79+21076x^80+25916x^81+30436x^82+31586x^83+31690x^84+26848x^85+21357x^86+14968x^87+9814x^88+5884x^89+2820x^90+1362x^91+667x^92+240x^93+115x^94+42x^95+41x^96+16x^97+9x^98+6x^99+2x^102+1x^106

The gray image is a code over GF(2) with n=664, k=18 and d=296.
This code was found by Heurico 1.16 in 705 seconds.