The generator matrix

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

generates a code of length 98 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+124x^88+1018x^89+2534x^90+4718x^91+7201x^92+10816x^93+15716x^94+20000x^95+26222x^96+27650x^97+30234x^98+28098x^99+25506x^100+21062x^101+15751x^102+10446x^103+7125x^104+3744x^105+2102x^106+1140x^107+431x^108+252x^109+115x^110+46x^111+44x^112+16x^113+12x^114+12x^115+2x^117+4x^119+2x^120

The gray image is a code over GF(2) with n=784, k=18 and d=352.
This code was found by Heurico 1.16 in 870 seconds.