The generator matrix

 1  0  0  1  1  1  2  1  1 X+2  1  1  0  2  0  X  1  1  X X+2  1  1  1  1  1  X  1  0  1  1 X+2  1  1 X+2  1  0  1  1  X  1  1  2  1  2  X  1  1  X  1  X X+2  1  1  1  1  1  1  1  1  2  1  1  1 X+2  1  2  1  1  0  1  2  1 X+2  0  1  X X+2  1  1  1  0  1  1  1  1  1 X+2  1
 0  1  0  2  3  1  1  0  2  0  3  1  1  1 X+2  X  X X+1  1  1 X+2 X+3 X+2 X+3  0  1  3  1  X X+3  1  X X+1  1 X+2  2  2  1  1 X+3 X+2  1  1  X  2  1  X X+2 X+1  1  1  0  2 X+3 X+1  3  3  2  0 X+2 X+1  2  2  X X+2  1  X  0  1 X+3  2  X  2  1 X+2  1  1  3  0  X  1 X+1  3  1  1 X+1 X+2  0
 0  0  1 X+3 X+1  2 X+1 X+2  1  1  3  X X+2  3  1  1  X X+1  3  X X+3  0  0  1 X+3  0  2  3  1  X X+1 X+1  2  1  1  1  2 X+3  X  3  X  2  3  1  1 X+2  2  1 X+2  2 X+3  3 X+2 X+2  0 X+2  0  X  1  1  X  0 X+1  1 X+2 X+3  0  2 X+3 X+1  1 X+3  1  1  2 X+3  3  X  X  3  X  2  2  0  1  3  1  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+44x^85+122x^86+96x^87+60x^88+68x^89+30x^90+40x^91+16x^92+8x^93+23x^94+1x^96+1x^100+1x^110+1x^116

The gray image is a code over GF(2) with n=352, k=9 and d=170.
This code was found by Heurico 1.13 in 0.219 seconds.