The generator matrix

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

generates a code of length 82 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+99x^78+176x^79+173x^80+152x^81+90x^82+76x^83+31x^84+36x^85+32x^86+36x^87+50x^88+20x^89+32x^90+8x^91+1x^94+8x^95+1x^98+1x^100+1x^114

The gray image is a code over GF(2) with n=328, k=10 and d=156.
This code was found by Heurico 1.16 in 0.336 seconds.