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  X  0  X X^2+2  X  0  X X^2+2  X  X  X  2  X  X  X X^2  X  X  2 X^2  1  1  1  1  1  1  1  1  X  X  X  X  1  1  1  1  1  1  1  1 X^2  0  0 X^2 X^2 X^2  2  2  1  1  1  1  1  1  1  1
 0  X X^2+2 X^2+X  0 X^2+X X^2+2 X+2  2 X^2+X+2 X^2 X+2  2 X^2+X+2 X^2  X  0 X^2+X X^2+2 X+2  0 X^2+X X^2+2 X+2  2 X^2+X+2 X^2  X  2 X^2+X+2 X^2  X X^2+X  X X+2  X X^2+X  X X+2  X  0 X^2+2 X^2+X+2  X  X  2 X^2  X X^2+X+2  X  X  X  0 X^2+2  2 X^2  0 X^2+2  2 X^2  0 X^2+2  2 X^2 X^2+X X+2 X^2+X 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 X^2 X^2  0  0  2  2 X^2+X X^2+X X^2+X+2 X^2+X+2
 0  0  2  2  2  0  0  2  2  2  0  0  0  0  2  2  0  0  2  2  2  2  0  0  2  2  0  0  0  0  2  2  0  2  2  0  2  0  0  2  2  2  2  0  0  2  2  2  0  2  2  0  0  0  0  0  2  2  2  2  0  0  0  0  0  2  2  0  2  0  0  2  2  0  2  0  2  0  2  0  0  2  2  0  0  2  2  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+246x^88+4x^92+4x^100+1x^112

The gray image is a code over GF(2) with n=704, k=8 and d=352.
This code was found by Heurico 1.16 in 0.766 seconds.