The generator matrix

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

generates a code of length 87 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 78.

Homogenous weight enumerator: w(x)=1x^0+480x^78+1734x^79+3720x^80+6908x^81+10623x^82+15192x^83+21203x^84+25362x^85+29263x^86+31808x^87+29964x^88+27366x^89+21638x^90+14668x^91+10048x^92+6026x^93+3187x^94+1556x^95+756x^96+356x^97+149x^98+72x^99+29x^100+10x^101+4x^102+10x^103+5x^104+2x^105+2x^108+2x^109

The gray image is a code over GF(2) with n=696, k=18 and d=312.
This code was found by Heurico 1.16 in 751 seconds.