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

generates a code of length 89 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 90.

Homogenous weight enumerator: w(x)=1x^0+56x^90+5x^92+1x^96+1x^100

The gray image is a code over GF(2) with n=712, k=6 and d=360.
This code was found by Heurico 1.16 in 0.594 seconds.