The generator matrix

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

generates a code of length 89 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+43x^82+250x^83+311x^84+472x^85+356x^86+390x^87+302x^88+352x^89+243x^90+278x^91+189x^92+220x^93+153x^94+144x^95+108x^96+116x^97+29x^98+50x^99+28x^100+22x^101+21x^102+6x^103+5x^104+2x^109+2x^110+1x^114+2x^115

The gray image is a code over GF(2) with n=356, k=12 and d=164.
This code was found by Heurico 1.16 in 1.5 seconds.