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

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+27x^78+44x^79+68x^80+90x^81+78x^82+80x^83+50x^84+36x^85+19x^86+4x^87+9x^88+2x^89+3x^90+1x^154

The gray image is a code over GF(2) with n=328, k=9 and d=156.
This code was found by Heurico 1.16 in 0.304 seconds.