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  0  2  0  2  0  0  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  X  X  0  2  X  0  X  X  X  2  X  0  0  2  X  X  1
 0  X  0  0  0  X  X  X  0  0  0  0  X  X  X  X  0  0  0  0  X  X  X  X  0  0  0  0  X  X  X  X  2  2  2  2  2  2  2 X+2  2 X+2  2 X+2  2 X+2  2 X+2  2 X+2  2 X+2  2 X+2  2 X+2  2 X+2 X+2  2  2 X+2 X+2  2  2 X+2  2 X+2  2 X+2  X  X  X  X  X  0  X  0  0  X  X  0  0  X  X  2  0  0
 0  0  X  0  X  X  X  0  0  0  X  X  X  X  0  0  2  2 X+2 X+2 X+2 X+2  2  2  2  2 X+2 X+2 X+2 X+2  2  2  X  X  2  X  X  0  2 X+2  0  X X+2  2  X  0  2 X+2  2 X+2  X  2  X  2  0  X X+2  X  0  2  X  0 X+2  0  0  X X+2  0 X+2  2  X  0 X+2  0  2  X X+2 X+2  2 X+2  0  0  X  2  0  X  0  0
 0  0  0  X  X  0  X  X  2 X+2 X+2  2  2 X+2 X+2  2  2  X X+2  0  2  X X+2  0  0 X+2  X  2  0 X+2  X  2  2 X+2  X  0  X  X  0  0  X  X  X  X  0  0  2  2 X+2  X X+2  0  2 X+2  2  2  2 X+2  X  X  X  2 X+2  0 X+2  0 X+2 X+2  0  2  0 X+2 X+2  0 X+2 X+2  0  2 X+2  0 X+2  2  2  X  X  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+23x^84+176x^85+23x^86+30x^88+138x^89+30x^90+7x^92+60x^93+7x^94+3x^96+10x^97+3x^98+1x^130

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 0.395 seconds.