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

generates a code of length 95 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 94.

Homogenous weight enumerator: w(x)=1x^0+26x^94+192x^95+31x^96+6x^110

The gray image is a code over GF(2) with n=760, k=8 and d=376.
This code was found by Heurico 1.16 in 0.765 seconds.