The generator matrix

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

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+60x^83+191x^84+196x^85+239x^86+196x^87+231x^88+146x^89+168x^90+118x^91+136x^92+46x^93+79x^94+62x^95+47x^96+42x^97+22x^98+6x^99+13x^100+10x^101+12x^102+6x^103+13x^104+4x^105+4x^109

The gray image is a code over GF(2) with n=356, k=11 and d=166.
This code was found by Heurico 1.11 in 0.484 seconds.