The generator matrix

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

generates a code of length 86 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 82.

Homogenous weight enumerator: w(x)=1x^0+120x^82+150x^83+255x^84+100x^85+90x^86+44x^87+26x^88+16x^89+37x^90+42x^91+59x^92+24x^93+35x^94+4x^95+6x^96+4x^97+4x^100+5x^102+1x^106+1x^112

The gray image is a code over GF(2) with n=344, k=10 and d=164.
This code was found by Heurico 1.11 in 0.385 seconds.