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

generates a code of length 97 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 93.

Homogenous weight enumerator: w(x)=1x^0+68x^93+60x^94+58x^95+339x^96+32x^97+311x^98+48x^99+8x^100+28x^101+44x^102+20x^103+4x^104+2x^127+1x^130

The gray image is a code over GF(2) with n=776, k=10 and d=372.
This code was found by Heurico 1.16 in 1.26 seconds.