The generator matrix

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

generates a code of length 82 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 76.

Homogenous weight enumerator: w(x)=1x^0+31x^76+152x^77+234x^78+264x^79+247x^80+194x^81+170x^82+142x^83+123x^84+110x^85+74x^86+44x^87+66x^88+52x^89+38x^90+34x^91+25x^92+18x^93+8x^94+12x^95+2x^96+2x^97+4x^98+1x^100

The gray image is a code over GF(2) with n=328, k=11 and d=152.
This code was found by Heurico 1.11 in 0.371 seconds.