The generator matrix

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

generates a code of length 86 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+242x^81+130x^82+346x^83+107x^84+312x^85+108x^86+248x^87+72x^88+150x^89+30x^90+98x^91+28x^92+52x^93+8x^94+20x^95+14x^96+36x^97+12x^98+24x^99+8x^101+1x^104+1x^108

The gray image is a code over GF(2) with n=344, k=11 and d=162.
This code was found by Heurico 1.16 in 9.85 seconds.