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  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  1  0  1  X  0  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  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  2 X+2  2  X  2 X+2  2  X  2 X+2  2  X  2 X+2  2  X  0 X+2  0 X+2  0 X+2  2  X  0 X+2  0  0 X+2 X+2 X+2  2  0  2  X  X X+2  X  X 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  2  0  2  0  2  0  2  0  2  0  2  0  2  0  2  0  0  2  0  2  0  2  0  2  0  2  0  2  0  2  0  2  0  0  0  0  0  2  0  2  0  0  2  2  0  2  2  2  0  2  2  2  0  0  2  2
 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  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  2  2  2  2  0  0  0  2  2  0  0  2  2  2  0  0  0  0  0  2
 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  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  2  2  0  2  2  2  0  2  2  0  2  0  2  0  0  0  2  2  0  0  2
 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  2  2  0  0  0  0  2  2  2  0  0  2  0  2  2  0  2  2  0  0  0  2  2  0  2  2  0  0  0  0  2  2  2  0  0  2  0  0  2  2  0  0  2  2  2  2  0  0  0  0  0  2  2  2  0  0  2  2  2  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+54x^84+96x^86+215x^88+96x^90+42x^92+7x^96+1x^168

The gray image is a code over GF(2) with n=352, k=9 and d=168.
This code was found by Heurico 1.16 in 0.525 seconds.