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  1  1  1  X  1  1  1  X  1  1  1
 0  X  0 X+2  0 X+2  0  X  0 X+2  0  X  0 X+2  0  X  0 X+2  0  X  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  2 X+2  2 X+2  2 X+2  2  X  2  X  2  X  2 X+2  2  X  0 X+2  0 X+2  0 X+2  2  X  0 X+2  0  0 X+2 X+2  X  2  2  2  0  0
 0  0  2  0  0  0  2  0  0  0  0  0  2  0  2  0  0  2  0  2  0  2  0  2  2  2  2  2  2  2  2  2  2  0  2  0  2  0  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  0  0  0  0  0  2  0  2  0  0  2  2  0  2  2  2  0  2  0  0
 0  0  0  2  0  0  0  2  0  0  0  0  0  2  0  2  2  2  2  2  2  2  2  2  2  0  2  0  2  0  2  0  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  2  2  2  0  0  2  2  2  2  0  0  0  0  0  0  0  0  0  0  2  2  2  2  0  0  0  2  2  0  0  0  2  2  2  0
 0  0  0  0  2  0  2  0  0  2  2  2  2  2  0  2  2  0  2  0  0  2  0  2  0  2  0  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  2  2  0  0  0  0  0  0  0  2  2  0  2  2  2  0  2  2  0  2  0  0  0  0  2  2
 0  0  0  0  0  2  0  2  2  2  2  0  2  0  2  2  0  0  2  2  2  0  0  2  0  2  2  0  2  2  0  0  0  0  2  2  2  0  0  2  0  2  2  0  2  2  0  0  2  2  2  2  0  0  0  0  0  0  2  2  2  0  0  2  0  0  2  2  0  0  2  2  2  2  0  0  0  2  2  2  2  0  2  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+39x^80+64x^82+64x^83+191x^84+64x^85+48x^86+24x^88+16x^90+1x^164

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 0.441 seconds.