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  X  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  1  X  1  1  1  2  1  0  1  1  1  X  1  1  1  1  1  1  0  X  1 X^2+2  1  1  X  1 X^2  X  1  1  1  X  X  1  1  1 X^2  1
 0  X  0  X  0  2 X+2  X X^2 X^2+X X^2 X^2+X+2 X^2 X^2+2 X^2+X+2 X^2+X+2  0 X^2+2  X X^2+X+2  X X^2  X  2  2  2 X+2 X^2 X^2+X+2 X^2+X X^2+X+2 X^2 X+2  0 X^2+2  2 X+2 X^2+X+2 X+2  0 X^2+X X^2 X^2 X^2+X+2 X^2  2 X^2+X+2 X^2+X  0 X+2  X X^2+X  2 X+2  X  2  2 X^2 X^2+X+2 X^2  X X^2 X+2 X^2+X  2 X+2  X  X X^2+X+2  2  2 X^2  2 X^2 X^2+2 X^2 X^2+X X^2+X+2 X^2+X+2 X^2+2 X^2+X+2 X^2+2 X+2 X+2  0 X^2  0
 0  0  X  X X^2+2 X^2+X+2 X^2+X X^2 X^2 X^2+X+2  X  0  2 X^2+X+2 X+2 X^2  0 X+2  X X^2 X^2+X+2 X^2 X^2  X X^2+X+2 X^2+2  0 X^2+X+2 X^2+X X+2  0  0  2 X^2+X  2 X+2 X^2+X X+2 X^2+2 X^2 X^2+2 X+2 X^2+X X+2 X^2+X+2  0 X^2+2  0 X^2+2 X+2 X+2 X^2+X X^2+X  X X^2+2  2  X X+2  0 X^2  X  2 X^2 X^2+X+2  X X^2+X X^2+X  0  X  2  X  X X^2+2 X+2  2  X X^2  2  2  2 X+2 X+2  2  0  X  X  2
 0  0  0  2  0  0  2  0  2  0  2  2  2  2  0  2  0  2  0  2  0  0  2  0  2  2  0  0  2  2  0  2  2  2  0  2  2  2  0  2  0  0  2  0  0  2  2  2  0  0  0  0  2  2  2  2  0  0  0  0  2  0  2  2  2  0  2  2  0  0  0  0  0  2  2  2  0  2  0  2  2  0  2  0  2  0  0
 0  0  0  0  2  2  2  2  2  2  0  0  0  2  0  2  2  2  0  0  2  0  2  2  0  0  2  0  2  0  0  2  0  0  2  2  0  2  0  2  2  0  0  2  2  0  0  2  0  2  2  0  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  2  0  0  0  0  2  2  2  2  0  0  0  0  0  0  2  0  2  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+90x^81+200x^82+250x^83+355x^84+294x^85+724x^86+516x^87+660x^88+220x^89+293x^90+138x^91+107x^92+82x^93+54x^94+52x^95+24x^96+18x^97+9x^98+4x^99+4x^100+1x^144

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 1.12 seconds.