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

generates a code of length 84 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+16x^80+46x^81+62x^82+86x^83+108x^84+88x^85+46x^86+24x^87+17x^88+10x^89+3x^90+2x^91+2x^92+1x^162

The gray image is a code over GF(2) with n=336, k=9 and d=160.
This code was found by Heurico 1.16 in 0.332 seconds.