The generator matrix

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

generates a code of length 89 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 85.

Homogenous weight enumerator: w(x)=1x^0+112x^85+134x^86+228x^87+107x^88+120x^89+51x^90+76x^91+19x^92+32x^93+41x^94+20x^95+15x^96+32x^97+12x^98+4x^99+1x^100+8x^101+1x^102+8x^103+1x^112+1x^114

The gray image is a code over GF(2) with n=356, k=10 and d=170.
This code was found by Heurico 1.16 in 0.446 seconds.