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

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+34x^81+83x^82+21x^84+24x^85+71x^86+7x^88+4x^89+5x^90+3x^92+1x^110+2x^113

The gray image is a code over GF(2) with n=336, k=8 and d=162.
This code was found by Heurico 1.16 in 0.416 seconds.