The generator matrix

 1  0  1  1  1 X+2  1  1  X  1  1  2 X+2  1 X+2  1  1  1  0  1  1  1  1  2  2 X+2  2  X  0 X+2  0 X+2  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+2  1  0  1  1  0  1  2  X  X  2 X+2  X  0  1  0  2  X  1  X  1
 0  1  1 X+2 X+3  1  2 X+1  1  X  3  1  1  0  1 X+1  0 X+1  1  X  1  X  1  1  1  1  1  1  1  1  1  1  0 X+2  2  X X+1  3  0 X+2  2  X  2  X  0 X+3  1  X X+2 X+1  2  2  X  1  X  2  2 X+2  3  2 X+2  2  X X+1  2  1 X+3  1 X+3  X  1  1  1  1  X  1  1  1  1 X+1  1  1  1  1  1 X+2
 0  0  X  0 X+2  0  X  2  X X+2  0 X+2  2  2  X  2  X  X  2 X+2 X+2  2  0 X+2  0  0  X  X  0  0  X  X  0  0  X  X  2  2  0  0  X  X  0  0  X  X X+2  X X+2  X X+2  0  2 X+2  2  0 X+2 X+2  2  2  2 X+2 X+2  0 X+2  2  0  0  2 X+2  X  0  2  0 X+2 X+2  2  2  0  2  X X+2  2  0  X  2
 0  0  0  2  0  0  0  2  2  0  2  0  0  2  2  0  2  2  2  2  2  0  0  0  2  2  0  2  0  2  0  2  0  0  0  2  2  0  2  2  0  2  2  2  2  0  2  2  0  0  0  0  2  2  0  2  2  0  0  0  0  2  0  2  0  0  0  2  0  2  2  2  0  2  0  2  0  2  0  2  2  2  2  0  0  0
 0  0  0  0  2  0  0  0  0  2  2  0  2  2  2  0  2  2  2  0  0  2  2  2  0  2  0  2  2  0  2  0  0  2  2  2  2  0  0  2  0  0  2  0  0  0  2  2  0  2  2  2  2  0  0  0  0  0  2  2  0  2  2  2  2  2  0  2  2  2  2  0  0  0  0  2  0  0  2  2  0  2  2  2  2  2
 0  0  0  0  0  2  2  2  0  2  2  0  2  0  0  2  2  0  2  2  0  0  2  0  2  0  2  2  0  0  2  2  2  2  0  0  2  2  2  2  0  0  2  2  2  2  2  2  2  2  2  0  0  2  0  0  0  0  2  2  2  0  0  0  0  0  0  0  0  0  0  2  2  2  2  0  0  2  2  0  2  2  2  0  0  2

generates a code of length 86 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 80.

Homogenous weight enumerator: w(x)=1x^0+155x^80+144x^81+231x^82+120x^83+215x^84+136x^85+179x^86+96x^87+158x^88+144x^89+175x^90+104x^91+88x^92+24x^93+39x^94+12x^96+14x^98+9x^100+2x^102+1x^112+1x^128

The gray image is a code over GF(2) with n=344, k=11 and d=160.
This code was found by Heurico 1.16 in 0.761 seconds.