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

generates a code of length 82 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 79.

Homogenous weight enumerator: w(x)=1x^0+64x^79+193x^80+49x^82+32x^83+104x^84+8x^86+32x^87+22x^88+6x^90+1x^130

The gray image is a code over GF(2) with n=328, k=9 and d=158.
This code was found by Heurico 1.16 in 48.2 seconds.