The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+170x^81+784x^82+1334x^83+1748x^84+1828x^85+2042x^86+1738x^87+1766x^88+1468x^89+1109x^90+848x^91+560x^92+408x^93+322x^94+112x^95+87x^96+14x^97+13x^98+14x^99+13x^100+2x^102+2x^103+1x^108

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 4.44 seconds.