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

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+19x^80+156x^81+29x^82+60x^83+30x^84+72x^85+24x^86+24x^87+12x^88+60x^89+10x^90+12x^91+2x^92+1x^130

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 0.437 seconds.