The generator matrix

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

generates a code of length 98 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 95.

Homogenous weight enumerator: w(x)=1x^0+358x^95+311x^96+394x^97+234x^98+268x^99+121x^100+164x^101+77x^102+58x^103+10x^104+14x^105+8x^106+16x^107+4x^108+4x^109+4x^115+1x^124+1x^142

The gray image is a code over GF(2) with n=784, k=11 and d=380.
This code was found by Heurico 1.16 in 7.2 seconds.