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

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+86x^89+63x^90+72x^91+260x^92+102x^93+251x^94+48x^95+53x^96+50x^97+5x^98+8x^99+3x^100+18x^101+1x^102+2x^112+1x^132

The gray image is a code over GF(2) with n=744, k=10 and d=356.
This code was found by Heurico 1.16 in 0.984 seconds.