The generator matrix

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

generates a code of length 84 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+62x^81+40x^82+174x^83+42x^84+64x^85+40x^86+80x^87+2x^88+2x^97+2x^99+1x^100+1x^112+1x^116

The gray image is a code over GF(2) with n=336, k=9 and d=162.
This code was found by Heurico 1.16 in 0.429 seconds.