The generator matrix

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

generates a code of length 93 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 90.

Homogenous weight enumerator: w(x)=1x^0+400x^90+288x^91+276x^92+272x^93+328x^94+144x^95+182x^96+48x^97+48x^98+16x^99+19x^100+16x^102+8x^106+1x^128+1x^132

The gray image is a code over GF(2) with n=744, k=11 and d=360.
This code was found by Heurico 1.16 in 34.5 seconds.