The generator matrix

 1  0  0  0  1  1  1  2  0  1  1  1  2  1  2  0  2  2  1  2  1  2  2  1  0  1  1  1  1  0  1  X  1  1 X+2  X  1  1  0  1  X  0  1  1 X+2 X+2  1 X+2  2  X  X X+2  X  1  1  1  1  1 X+2  1  1  1  1  2  X  1  1  X X+2  1  1 X+2  0  X  1  1  X  2  1  1  1  1 X+2  1  1  1
 0  1  0  0  0  2  2  2  1 X+3 X+1 X+3  1 X+1  1  1  1  0  2  2 X+3  1  1  1  X X+2  3  X  2  1  1  1  X  3  1  X X+2  1  1  X  2 X+2  0 X+3  X  1  3 X+2  1  2  1  1  2 X+2  X X+1 X+1  1  X  2 X+3  3 X+2  1  1  0  2  2  1 X+1 X+2  1 X+2 X+2 X+1  X  1  0  1  0  3 X+1  0 X+2  1  0
 0  0  1  0  2  1  3  1 X+1  1  2  3 X+1  0  0  2 X+3  1  0  1  2  2  1  2  2  0  1 X+1 X+1  3 X+1  X X+2  1  3  1  2 X+2  1  3 X+2 X+2 X+1 X+2  1  2 X+3  1  X  1 X+2  3  1  X  2  1 X+1  X  X X+3  X  3  0 X+1  0 X+2 X+2  0  0  X X+1 X+2  1  2 X+2 X+1 X+1  1 X+2  3  2 X+2 X+2 X+2  X X+2
 0  0  0  1 X+3 X+3  0 X+1  2  0  2 X+3  1 X+1  3  X X+1  X X+2  1  X X+3  2 X+1  1  1  1 X+1  2  1  0  2 X+3 X+1  2 X+2 X+2 X+2 X+1 X+1  1  1  X  3 X+1  1 X+3  2  X X+1  X  0  2  1 X+3  3 X+2 X+3  1  X X+1  2  X X+2  2  X X+1  1 X+2  X  2  1  X  1  0 X+2 X+3 X+1  3  3  3 X+3  1  2  1  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+243x^80+304x^81+526x^82+352x^83+484x^84+212x^85+418x^86+220x^87+256x^88+168x^89+220x^90+108x^91+195x^92+80x^93+118x^94+44x^95+59x^96+32x^97+26x^98+12x^99+9x^100+4x^101+4x^102+1x^104

The gray image is a code over GF(2) with n=344, k=12 and d=160.
This code was found by Heurico 1.16 in 4.29 seconds.