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

generates a code of length 88 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 79.

Homogenous weight enumerator: w(x)=1x^0+476x^79+1816x^80+3876x^81+6879x^82+10620x^83+15400x^84+20848x^85+25770x^86+29700x^87+31033x^88+29862x^89+26361x^90+21108x^91+15906x^92+10526x^93+5878x^94+3110x^95+1578x^96+726x^97+340x^98+146x^99+87x^100+60x^101+18x^102+2x^103+2x^104+4x^105+2x^106+6x^107+2x^109+1x^116

The gray image is a code over GF(2) with n=704, k=18 and d=316.
This code was found by Heurico 1.16 in 775 seconds.