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

generates a code of length 87 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+282x^81+256x^82+498x^83+346x^84+506x^85+259x^86+380x^87+201x^88+280x^89+207x^90+240x^91+141x^92+164x^93+45x^94+88x^95+42x^96+42x^97+29x^98+38x^99+5x^100+34x^101+4x^102+4x^103+4x^105

The gray image is a code over GF(2) with n=348, k=12 and d=162.
This code was found by Heurico 1.16 in 29.8 seconds.