The generator matrix

 1  0  1  1  1  2  1  1  X  1  1  X  1  1  0  1  1  0  1  1  X  1  1  X  1  1  X  1  2  1  1  0  1 X+2  1  1  2  1  1 X+2  1  1  1  2  1  1  1  X  X  X  1  X  1  1 X+2 X+2  1  2  1 X+2  1  1  1  1  1  1  1  2 X+2  1 X+2 X+2  1  1  1  1  1 X+2  1  1  1  1  X  1  1  1
 0  1  1  0 X+1  1 X+3  0  1  2  1  1  0 X+1  1  2 X+1  1  0  1  1  0  1  1 X+2 X+3  1 X+2  1  1 X+1  1  3  1  X X+2  1 X+3  3  1  X X+2 X+3  1 X+2  X  1  1  2  0  0  2  X  0  1  1  X  1  3  1  0  3 X+2  3  2  1  3  1  1  0  1  1 X+3 X+3  1 X+2  2  1 X+2  X  0 X+2  2  1  1  2
 0  0  X  0  0  0  0  X  X  X  X  X  2  2  2  2  2  2 X+2 X+2 X+2 X+2 X+2 X+2  X  X  0  0 X+2  2  X  X  0  0  0 X+2 X+2 X+2  2  2  X  2 X+2  X  2 X+2  0  2 X+2  X  2  2  0  X  X  2  0  2  0 X+2  X X+2 X+2  X X+2  2  X  X  2  2  X  0 X+2  2  2 X+2  2  X  2  2 X+2  2  X X+2  0  0
 0  0  0  X  2 X+2 X+2  X  2  2 X+2  X  2  0  2 X+2  X  X  0  X X+2 X+2  2  0  X  0  X  0  2  X X+2  X  0  2 X+2  0  X X+2  0  2  0 X+2  0  2  0  X  X  X  2 X+2 X+2 X+2  0  2  X X+2  X  2 X+2  2  0  X X+2  0 X+2  0  2  0  X  X X+2  0  X X+2  2  2  0  2  X X+2  X  2  2  0 X+2 X+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+44x^81+115x^82+132x^83+143x^84+116x^85+70x^86+98x^87+80x^88+64x^89+38x^90+16x^91+43x^92+28x^93+9x^94+6x^95+4x^96+2x^97+4x^98+4x^99+3x^102+2x^105+1x^112+1x^114

The gray image is a code over GF(2) with n=344, k=10 and d=162.
This code was found by Heurico 1.16 in 0.408 seconds.