The generator matrix

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

generates a code of length 93 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 89.

Homogenous weight enumerator: w(x)=1x^0+128x^89+63x^90+260x^91+193x^92+808x^93+190x^94+192x^95+61x^96+120x^97+3x^98+28x^99+1x^180

The gray image is a code over GF(2) with n=744, k=11 and d=356.
This code was found by Heurico 1.16 in 1.05 seconds.