The generator matrix

 1  0  0  1  1  1  2  0  0  2  1  1  1  1  X  1  0  1  1  2  1  1  0  2  1  1  1  0  0  0 X+2  X X+2  X X+2  X X+2  X  1  1  1  1  X  1  1  1  1  1  1  1  1  1  1  1  2  1  X X+2  1  1  1  1  1  1  1  1  X X+2  X X+2 X+2 X+2 X+2 X+2  0  2  0  2  0  2  X  X  2  0
 0  1  0  0  1  1  1  X  1  1  X X+1  X X+1  1  1  2  1  X  1 X+1  X  1  1  0  0 X+1  1  2 X+2  1  1  1  1  1  1  1  0  X X+1  X X+1  X  2  3  2 X+1  3 X+2  0 X+3  0  1  1  X  X  2  X X+3 X+2 X+2 X+3  X X+2 X+1 X+3  X  0 X+2  2  0  X  2 X+2  X  0 X+2  2  1  1  1  1  0  X
 0  0  1  1  2  3  1  1  X X+1  2  1  3  0  0 X+3  1 X+2 X+2  3 X+1 X+3  2 X+1 X+1  X  X  X  1  1  1  X X+1  1  0 X+3 X+2  1  0 X+2  1 X+3  1 X+3 X+2  0  3  3 X+3 X+2  2  1  2 X+3  1 X+2  1  1 X+1 X+2  0 X+3  2  X X+1 X+3  1  1  1  1  1  1  1  1  1  1  1  1  1  0  2 X+1  1  1
 0  0  0  2  0  2  2  2  2  0  2  0  0  2  0  2  2  0  2  0  0  0  2  2  2  0  2  0  0  2  0  0  0  2  2  2  2  0  0  0  2  2  0  0  2  2  2  0  2  2  0  0  2  0  0  0  2  2  0  2  0  2  0  2  2  0  2  0  2  0  2  0  2  0  0  2  0  2  0  0  2  0  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+115x^80+96x^81+316x^82+96x^83+116x^84+28x^86+80x^88+32x^89+84x^90+32x^91+20x^92+4x^94+1x^100+2x^108+1x^116

The gray image is a code over GF(2) with n=336, k=10 and d=160.
This code was found by Heurico 1.11 in 0.356 seconds.