The generator matrix

 1  0  0  1  1  1 X+2  X  1  1  1  1  X  2  1  1  0  1  1  0  X  1  1  X X+2  1  1  X  1  1 X+2 X+2  2  1  0  1  1  1  1  X  0  2  1  2  1  1  2  1  1  0  1 X+2  1  1  X  1  X  2  1  0  1  1 X+2  1  1  2 X+2  1  0  1  1  1 X+2  1 X+2  1 X+2  1  0  X  X  1  1  1 X+2  1
 0  1  0  0  3 X+1  1  2  2  2 X+3  1  1  1  0  2  0  1  3  1  1 X+2  X  X  1 X+1 X+3  1 X+2  X  X  1  1 X+3 X+2 X+2 X+1  X  1  1  1  1  0  1  0  3 X+2  2 X+1  1 X+2  1  X  1  1  3 X+2  1 X+3  0  2 X+3  0  X  2  1  1  3  1 X+1  1 X+3  2  2  0 X+1  1 X+3  1  X  1  X  1 X+3  1  0
 0  0  1  1  3  2  3  1  0 X+3 X+1  2  0  1  2 X+3  1  3  X X+2  1  X X+3  1 X+3 X+1 X+2 X+2  X X+1  1 X+3 X+1  0  1 X+2  X  1 X+3  X  1 X+3  X  2  X X+1  1 X+3  3  X  2  2  0  0  2 X+2  1  1  0  1  1 X+2  1  0  2 X+2 X+2 X+3  2  3 X+2  0  1 X+1  1  1  1  X X+2  1  2  X  X X+1 X+2  0
 0  0  0  X  X  0  X  X  X  0  0  X  X  0  2  2  2  0  0  0  0 X+2 X+2  X  X X+2 X+2  X  X  X X+2  0  X  X  0  2  2  0  2  2 X+2  0  2  X X+2 X+2 X+2  X X+2 X+2 X+2  2  0  2 X+2  X  0  2  2  X  0  2  2  2 X+2  X X+2  0  2  X  2 X+2  0 X+2 X+2  0  2  X X+2 X+2  2  2  2  2  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+31x^80+170x^81+219x^82+344x^83+206x^84+158x^85+132x^86+156x^87+112x^88+108x^89+66x^90+68x^91+45x^92+90x^93+52x^94+34x^95+14x^96+18x^97+8x^98+4x^99+7x^100+2x^102+2x^103+1x^106

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 0.562 seconds.