The generator matrix

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

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+90x^94+106x^95+126x^96+254x^97+923x^98+230x^99+106x^100+114x^101+90x^102+7x^104+1x^194

The gray image is a code over GF(2) with n=784, k=11 and d=376.
This code was found by Heurico 1.16 in 1.26 seconds.