The generator matrix

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

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+185x^76+332x^77+384x^78+464x^79+533x^80+286x^81+333x^82+322x^83+260x^84+172x^85+170x^86+132x^87+131x^88+98x^89+70x^90+70x^91+57x^92+24x^93+34x^94+20x^95+9x^96+9x^98

The gray image is a code over GF(2) with n=328, k=12 and d=152.
This code was found by Heurico 1.11 in 0.575 seconds.