The generator matrix

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

generates a code of length 93 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+180x^88+700x^89+1135x^90+1114x^91+1030x^92+1062x^93+762x^94+504x^95+506x^96+328x^97+250x^98+258x^99+142x^100+86x^101+63x^102+28x^103+17x^104+16x^105+5x^106+3x^108+1x^110+1x^116

The gray image is a code over GF(2) with n=744, k=13 and d=352.
This code was found by Heurico 1.16 in 1.47 seconds.