The generator matrix

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

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+122x^81+193x^82+178x^83+175x^84+164x^85+209x^86+170x^87+137x^88+148x^89+117x^90+130x^91+97x^92+54x^93+65x^94+22x^95+18x^96+18x^97+6x^98+8x^99+4x^101+2x^102+2x^104+4x^107+2x^109+2x^120

The gray image is a code over GF(2) with n=348, k=11 and d=162.
This code was found by Heurico 1.16 in 0.853 seconds.