The generator matrix

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

generates a code of length 97 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 92.

Homogenous weight enumerator: w(x)=1x^0+85x^92+480x^93+503x^94+492x^95+365x^96+446x^97+332x^98+428x^99+366x^100+388x^101+99x^102+52x^103+14x^104+10x^105+12x^106+4x^107+4x^108+4x^110+4x^113+4x^116+1x^124+2x^130

The gray image is a code over GF(2) with n=776, k=12 and d=368.
This code was found by Heurico 1.16 in 1.41 seconds.