The generator matrix

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

generates a code of length 88 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+134x^84+92x^85+270x^86+80x^87+151x^88+22x^89+66x^90+4x^91+44x^92+44x^93+42x^94+12x^95+40x^96+2x^97+12x^100+5x^102+1x^104+1x^110+1x^120

The gray image is a code over GF(2) with n=352, k=10 and d=168.
This code was found by Heurico 1.16 in 0.429 seconds.