The generator matrix

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

generates a code of length 87 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 81.

Homogenous weight enumerator: w(x)=1x^0+164x^81+805x^82+1094x^83+2093x^84+1638x^85+2240x^86+1650x^87+1886x^88+1164x^89+1359x^90+652x^91+644x^92+402x^93+334x^94+128x^95+70x^96+4x^97+26x^98+6x^99+9x^100+4x^101+4x^102+6x^103+1x^104

The gray image is a code over GF(2) with n=696, k=14 and d=324.
This code was found by Heurico 1.16 in 4.16 seconds.