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

generates a code of length 89 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+28x^86+32x^87+39x^88+64x^89+32x^90+32x^91+16x^92+7x^96+4x^102+1x^120

The gray image is a code over GF(2) with n=356, k=8 and d=172.
This code was found by Heurico 1.16 in 0.52 seconds.