The generator matrix

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

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+131x^84+132x^85+204x^86+144x^87+122x^88+24x^89+40x^90+47x^92+48x^93+48x^94+32x^95+34x^96+6x^100+4x^101+4x^102+2x^108+1x^112

The gray image is a code over GF(2) with n=352, k=10 and d=168.
This code was found by Heurico 1.11 in 0.393 seconds.