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

generates a code of length 89 over Z4[X]/(X^2+2) 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.