The generator matrix

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

generates a code of length 83 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+108x^81+126x^82+88x^83+120x^84+24x^85+24x^87+6x^88+12x^89+2x^90+1x^128

The gray image is a code over GF(2) with n=332, k=9 and d=162.
This code was found by Heurico 1.16 in 35.8 seconds.