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  X  1  X  X  X  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  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X  X X^2  1  1  1
 0 X^2+2  0 X^2  0  0 X^2 X^2+2  0  0 X^2 X^2+2  0  0 X^2 X^2+2  0  0 X^2 X^2+2  0  0 X^2 X^2+2  0  0 X^2 X^2+2  0  0 X^2  2 X^2+2  2  2  2  2 X^2+2  2 X^2  2 X^2+2  2 X^2  2 X^2+2  2 X^2  2  2 X^2+2 X^2  2  2 X^2+2 X^2  2  2 X^2+2 X^2  2  2 X^2+2 X^2  2  2 X^2+2 X^2 X^2 X^2+2 X^2 X^2 X^2 X^2+2 X^2+2 X^2+2  0  0 X^2 X^2 X^2 X^2  0  0  0  0 X^2 X^2+2 X^2+2 X^2  0  0  2  2  0  2  2  0
 0  0 X^2+2 X^2  0 X^2+2 X^2  0  0 X^2+2 X^2  0  0 X^2+2 X^2  0  2 X^2 X^2+2  2  2 X^2 X^2+2  2  2 X^2 X^2+2  2  2 X^2 X^2+2 X^2  2 X^2 X^2 X^2  2 X^2+2 X^2  2  2 X^2+2 X^2  2  2 X^2+2 X^2  2  2 X^2 X^2+2  2  0 X^2+2 X^2  0  0 X^2+2 X^2  0  0 X^2+2 X^2  0  0 X^2+2 X^2  0 X^2  0 X^2+2  0 X^2  0 X^2+2  2 X^2+2 X^2 X^2  0 X^2+2  2  0  2 X^2+2 X^2 X^2+2 X^2  2  2  0  0  2  0  0 X^2 X^2 X^2+2
 0  0  0  2  0  0  2  0  2  2  0  2  2  2  0  2  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  0  0  2  2  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  0  0  2  2  0  0  2  2  0  0  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  0  0  2  0
 0  0  0  0  2  2  2  2  2  2  0  2  0  0  2  0  0  0  0  0  2  2  2  2  2  2  2  2  0  0  0  0  0  2  2  0  0  0  0  0  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  2  2  2  2  2  2  2  2  0  0  0  0  0  0  0  0  2  2  2  2  0  2  0  2  2  0  2  0  2  0  2  0  2  0  2  0  2  2  0  0  2  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+24x^94+174x^95+39x^96+536x^98+112x^99+24x^100+15x^102+96x^103+2x^127+1x^134

The gray image is a code over GF(2) with n=784, k=10 and d=376.
This code was found by Heurico 1.16 in 1.22 seconds.