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

generates a code of length 92 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+193x^88+96x^89+148x^90+288x^91+610x^92+288x^93+136x^94+96x^95+180x^96+4x^98+6x^100+1x^104+1x^176

The gray image is a code over GF(2) with n=736, k=11 and d=352.
This code was found by Heurico 1.16 in 1.77 seconds.