The generator matrix

 1  0  0  1  1  1  2  0  0  2  1  1  1  1  X  1  0  1  1  0  1  1  2  0  1  1  1  2  0  0  X  X  X X+2 X+2 X+2 X+2  X  1  1  1 X+2  1  1  1  1  1  1  1  1  1  1  1  1  2  1  X  X  1  1  1  1  1 X+2 X+2 X+2 X+2  2  0 X+2  1  1  1  1  X  1  1  X  2  1  1  1  1  1
 0  1  0  0  3  3  1 X+2  1  1  X X+3  X X+3  1  1 X+2 X+1 X+2  1 X+1  2  1  1 X+2  2  1  1  X  2  1  1  1  1  1  1  1  X  2  3  1  2 X+3  X  2 X+3  0 X+2 X+3 X+3  X  3  2 X+2  0  3  X  0  0  1  0  3  1  2 X+2  0 X+2 X+2  0  X X+3  1 X+2  1  1  0 X+3  1  X X+1  X  3  X X+2
 0  0  1 X+1 X+3  2 X+3  1 X+2  1  X X+2  1  3  1  3  1  2 X+1  0 X+3  X  1  X  0  1 X+2 X+1  1  1  X  2 X+3  X  3  0 X+3  1  2 X+3  0  1 X+1 X+3  3  X X+2  2  1  0  1  3 X+1  X  1 X+2  1  1  X  0  0  2  2  1  1  1  1  1  1  1 X+3  X  0 X+2 X+2 X+1  0 X+2  X  X X+2  X  2  2
 0  0  0  2  2  0  2  2  2  0  2  2  0  0  0  2  0  2  0  2  0  0  2  0  2  2  0  0  2  0  2  2  0  0  2  0  2  2  2  0  2  2  2  2  0  0  2  0  2  0  2  0  0  0  2  2  0  0  0  0  2  2  0  0  0  2  2  0  2  2  0  2  0  2  0  0  2  2  2  0  0  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+106x^80+198x^81+183x^82+90x^83+101x^84+56x^85+69x^86+28x^87+57x^88+34x^89+19x^90+18x^91+20x^92+16x^93+16x^94+1x^96+8x^97+1x^100+1x^104+1x^110

The gray image is a code over GF(2) with n=336, k=10 and d=160.
This code was found by Heurico 1.16 in 0.366 seconds.