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  0  1  1 X+2  1  1  0  1  1 X+2  1  1  0  1  1  0  1 X+2  1  1  1 X+2  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1  2  1  1  X  2  1  1  1  1  1  X  2  X  2  2  X
 0  1 X+1 X+2  1  1 X+1  0  1 X+2  3  1  0 X+1  1 X+2  3  1  0 X+1  1 X+2  1  1  0 X+1  1 X+2  3  1  0 X+1  1 X+2  1  1  0 X+1  1 X+2 X+1  1  3  1  0 X+2  1  1  2  X  2  X  2  X  2  X  2  X  2  X  2  X  2  X X+3  3 X+3  1 X+3  1 X+3  1  1 X+3  3  1  1 X+3  3 X+3  3 X+3  1  1  1  1  0  1
 0  0  2  0  0  0  0  2  2  2  2  2  0  0  0  2  2  2  2  2  2  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  0  0  0  2  2  2  0  0  2  0  2  2  2  2  2  2  0  0  0  0  2  2  2  2  0  0  0  0  2  0  2  0  2  2  0  0  2  2  2  2  2  0  0  0  2  0  0  2  0  0  2  0
 0  0  0  2  0  2  2  2  2  0  2  0  0  0  2  0  0  2  2  2  0  2  2  0  2  0  0  0  2  2  0  0  0  2  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  2  2  2  2  0  0  0  0  2  2  2  2  0  0  0  0  0  0  2  2  2  2  0  2  2  0  2  0  2  2  0  0  2  2  2  0  0  0
 0  0  0  0  2  0  2  2  2  2  0  2  2  0  2  0  2  0  0  2  0  2  0  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  0  2  2  0  0  2  2  0  2  0  0  2  2  0  0  2  0  2  2  0  2  0  0  2  0  0  2  2  2  2  0  2  0  0  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 85.

Homogenous weight enumerator: w(x)=1x^0+48x^85+30x^86+128x^87+62x^88+192x^89+32x^90+16x^93+1x^110+1x^112+1x^126

The gray image is a code over GF(2) with n=352, k=9 and d=170.
This code was found by Heurico 1.16 in 0.47 seconds.