The generator matrix

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

generates a code of length 82 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 77.

Homogenous weight enumerator: w(x)=1x^0+236x^77+144x^78+328x^79+97x^80+352x^81+104x^82+224x^83+36x^84+160x^85+74x^86+80x^87+20x^88+80x^89+20x^90+24x^91+28x^93+10x^94+16x^95+6x^96+8x^97

The gray image is a code over GF(2) with n=328, k=11 and d=154.
This code was found by Heurico 1.16 in 2.97 seconds.