The generator matrix

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

generates a code of length 81 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 79.

Homogenous weight enumerator: w(x)=1x^0+208x^79+61x^80+32x^81+62x^82+112x^83+32x^87+1x^96+2x^98+1x^112

The gray image is a code over GF(2) with n=324, k=9 and d=158.
This code was found by Heurico 1.16 in 1.84 seconds.