The generator matrix

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

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+91x^82+342x^83+279x^84+370x^85+675x^86+386x^87+656x^88+334x^89+265x^90+236x^91+48x^92+130x^93+11x^94+52x^95+6x^96+16x^97+12x^98+6x^99+4x^101+2x^102+2x^103+1x^104+1x^140

The gray image is a code over GF(2) with n=696, k=12 and d=324.
This code was found by Heurico 1.16 in 61.7 seconds.