The generator matrix

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

generates a code of length 89 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 83.

Homogenous weight enumerator: w(x)=1x^0+352x^83+202x^84+524x^85+190x^86+644x^87+185x^88+456x^89+158x^90+424x^91+96x^92+240x^93+78x^94+136x^95+61x^96+148x^97+18x^98+92x^99+22x^100+28x^101+4x^102+12x^103+9x^104+12x^105+4x^107

The gray image is a code over GF(2) with n=356, k=12 and d=166.
This code was found by Heurico 1.11 in 189 seconds.