The generator matrix

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

generates a code of length 89 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+25x^84+124x^85+92x^86+192x^87+116x^88+108x^89+56x^90+68x^91+39x^92+110x^93+32x^94+24x^95+11x^96+6x^97+2x^98+6x^100+2x^101+4x^103+2x^104+2x^105+2x^130

The gray image is a code over GF(2) with n=356, k=10 and d=168.
This code was found by Heurico 1.16 in 0.459 seconds.