The generator matrix

 1  0  1  1  1 X+2  1  1  0  1  1 X+2  1  1  0  1  1 X+2  1  1  0  1  1 X+2  1  1  2  1  1  X  1  1  2  1  1  X  1  1  1  1  2  X  1  1  1  1  2  X  X  X  0  X  X  0  X  X  0  1  1  1  1  2  X  X  1  1  2  2  1  1  0 X+2  2  X  0  0  2  2 X+2  X  0  X  1  1  1  1  X  X
 0  1 X+1 X+2  3  1  0 X+1  1 X+2  3  1  0 X+1  1 X+2  3  1  0 X+1  1 X+2  3  1  2 X+3  1  X  1  1  2 X+3  1  X  1  1  2  X X+3  1  1  1  2  X X+3  1  1  1  0 X+2  X X+2  0  X  0 X+2  X  0  2 X+1 X+3  X  2  X  0  2  X  X X+1 X+3  1  1  1  1  2  1  1  X  1  1  X  2 X+1 X+3 X+1 X+3  0  0
 0  0  2  0  2  0  2  0  2  2  0  2  0  0  0  2  0  0  2  2  2  0  2  2  2  2  2  2  2  2  0  0  0  0  0  0  2  2  2  2  2  2  0  0  0  0  0  0  0  2  0  2  2  2  2  0  2  0  2  0  2  0  0  0  0  2  2  2  0  2  0  0  0  0  0  2  2  0  2  2  0  0  2  0  2  0  0  2
 0  0  0  2  2  2  2  0  0  0  2  2  2  2  2  2  0  0  0  2  2  0  0  0  0  0  0  2  2  2  2  2  2  0  0  0  2  0  2  0  2  0  0  2  0  2  0  2  2  2  2  0  2  0  0  2  2  0  0  0  2  2  2  2  2  2  2  0  2  0  0  0  0  0  2  2  0  0  2  0  0  0  2  2  0  0  0  2

generates a code of length 88 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+50x^86+96x^87+42x^88+10x^90+32x^91+12x^92+2x^94+9x^96+2x^106

The gray image is a code over GF(2) with n=352, k=8 and d=172.
This code was found by Heurico 1.16 in 0.373 seconds.