The generator matrix

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

generates a code of length 91 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 83.

Homogenous weight enumerator: w(x)=1x^0+802x^83+1705x^84+4060x^85+5555x^86+8888x^87+10298x^88+13086x^89+13412x^90+15658x^91+14060x^92+13630x^93+9979x^94+8166x^95+4845x^96+3480x^97+1571x^98+1008x^99+475x^100+260x^101+36x^102+66x^103+8x^104+10x^105+5x^106+4x^107+2x^109+2x^110

The gray image is a code over GF(2) with n=728, k=17 and d=332.
This code was found by Heurico 1.16 in 253 seconds.