The generator matrix

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

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+44x^80+180x^81+266x^82+240x^83+173x^84+180x^85+186x^86+146x^87+113x^88+82x^89+97x^90+80x^91+59x^92+66x^93+54x^94+22x^95+16x^96+14x^97+12x^98+8x^99+1x^100+6x^101+1x^106+1x^108

The gray image is a code over GF(2) with n=344, k=11 and d=160.
This code was found by Heurico 1.11 in 0.434 seconds.