The generator matrix

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

generates a code of length 98 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 94.

Homogenous weight enumerator: w(x)=1x^0+236x^94+716x^95+696x^96+564x^97+376x^98+436x^99+292x^100+160x^101+156x^102+172x^103+86x^104+108x^105+56x^106+20x^107+9x^108+8x^110+1x^112+2x^116+1x^124

The gray image is a code over GF(2) with n=784, k=12 and d=376.
This code was found by Heurico 1.16 in 0.672 seconds.