The generator matrix

 1  0  1  1  1 X^2+X  1  1 X^2+2  1  1 X+2  1  1  0  1  1 X^2+X  1  1 X^2+2  1  1 X+2  1  1  0  1  1 X^2+X  1 X^2+2  1  1  1 X+2  1  2  1  1 X^2  1  1 X^2+X  1  1  1 X+2  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  0 X^2+X+2 X^2+2  X  0 X^2+2 X^2+X  X X^2+X X^2 X+2  X  2
 0  1 X+1 X^2+X X^2+1  1 X^2+X+3 X^2+2  1 X+2  3  1  0 X+1  1 X^2+X X^2+1  1 X^2+2 X^2+X+3  1 X+2  3  1  0 X+1  1 X^2+X X^2+1  1 X^2+2  1 X^2+X+3 X+2  3  1  2  1 X+1 X^2+X  1 X^2+X+3 X^2+1  1 X^2 X+2  3  1 X^2+X+2  0  X X^2+2  0 X^2+X X^2+2 X+2 X+3 X^2+3 X^2+X+1  1 X+1 X^2+1 X+1 X^2+1 X^2+X+3  3 X^2+X+3  3 X+3 X^2+3 X^2+X+1  1  0 X^2+X  2 X^2+X+2 X^2+2 X+2 X^2  X  1  1  1  1  1  1  1  1  1  X  1  1  1
 0  0  2  0  0  0  0  2  2  2  2  2  0  0  0  2  2  2  2  2  2  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  0  0  0  2  2  2  0  0  2  0  2  2  2  2  0  0  2  0  0  2  2  2  0  0  0  0  2  2  0  0  0  0  2  2  2  2  2  0  2  2  0  0  0  2  2  2  0  0  2  0  0  2  2  0  0  2  2
 0  0  0  2  0  2  2  2  2  0  2  0  0  0  2  0  0  2  2  2  0  2  2  0  2  0  0  0  2  2  0  0  0  2  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  2  2  0  2  0  2  0  0  0  0  0  2  2  2  2  0  0  2  2  2  2  0  0  0  2  0  2  0  0  2  2  2  0  0  2  2  2  0  0  2  2  0  2  2
 0  0  0  0  2  0  2  2  2  2  0  2  2  0  2  0  2  0  0  2  0  2  0  2  2  2  2  2  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  0  0  0  0  2  0  0  2  2  0  2  0  2  0  2  0  2  0  2  0  0  2  0  2  0  2  0  2  2  2  0  2  0  2  0  0  0  0  0  0  2  2  2  2  2  0  0  0  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+316x^89+78x^90+80x^91+132x^92+864x^93+92x^94+104x^95+56x^96+292x^97+22x^98+8x^99+2x^120+1x^128

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 0.671 seconds.