The generator matrix

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

generates a code of length 83 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 79.

Homogenous weight enumerator: w(x)=1x^0+104x^79+191x^80+138x^81+180x^82+72x^83+65x^84+28x^85+49x^86+32x^87+29x^88+50x^89+58x^90+20x^91+4x^95+1x^102+1x^104+1x^116

The gray image is a code over GF(2) with n=332, k=10 and d=158.
This code was found by Heurico 1.11 in 33.9 seconds.