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

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

Homogenous weight enumerator: w(x)=1x^0+32x^89+18x^90+6x^92+4x^94+2x^98+1x^104

The gray image is a code over GF(2) with n=356, k=6 and d=178.
This code was found by Heurico 1.16 in 0.383 seconds.