The generator matrix

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

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+32x^81+104x^82+40x^83+20x^84+14x^85+28x^86+6x^87+3x^88+2x^90+2x^93+2x^94+2x^95

The gray image is a code over GF(2) with n=332, k=8 and d=162.
This code was found by Heurico 1.16 in 0.901 seconds.