The generator matrix

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

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+34x^76+40x^77+57x^78+122x^79+97x^80+120x^81+161x^82+92x^83+84x^84+82x^85+27x^86+34x^87+30x^88+12x^89+10x^90+8x^91+10x^92+2x^93+1x^154

The gray image is a code over GF(2) with n=328, k=10 and d=152.
This code was found by Heurico 1.16 in 0.478 seconds.