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

generates a code of length 89 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+42x^84+24x^86+64x^87+83x^88+128x^89+36x^90+64x^91+42x^92+19x^96+4x^98+4x^100+1x^168

The gray image is a code over GF(2) with n=356, k=9 and d=168.
This code was found by Heurico 1.16 in 0.546 seconds.