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

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

Homogenous weight enumerator: w(x)=1x^0+3x^88+50x^89+4x^90+6x^93

The gray image is a code over GF(2) with n=704, k=6 and d=352.
This code was found by Heurico 1.16 in 0.484 seconds.