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  1  1  1  1  1  1  1
 0  X  0 X^2+X X^2 X^2+X+2 X^2+2  X X^2 X^2+X  2 X+2  2 X^2+X+2 X^2+2 X+2  0 X^2+X X^2+2 X+2 X^2+X+2  2  X X^2 X^2+2 X^2+X+2 X+2  2  0 X^2+X X^2  X  0 X^2+X  0 X^2+X X^2  X X^2  X  0 X^2+X  0 X^2+X X^2+2 X+2 X^2+2 X+2  0 X^2+X X^2+2 X+2  2 X^2+X+2 X^2+2 X+2  0 X^2+X X+2 X^2+2  2 X^2+X+2 X^2+2 X+2  0 X^2 X^2+X  X  2 X^2+2 X^2+X+2 X+2  2  0 X^2+2 X^2 X^2+X+2 X+2 X^2+X+2  X X^2+X+2 X^2+X+2  2 X^2 X^2+2 X^2 X^2  X X+2  0  2  2
 0  0 X^2+2  0 X^2 X^2  0 X^2 X^2+2  0 X^2  0  0 X^2+2  0 X^2+2  2  2  2  2 X^2 X^2 X^2+2 X^2+2 X^2  2  2 X^2+2  2 X^2+2  2 X^2  0  0 X^2+2 X^2+2 X^2+2 X^2+2  0  2  2  2 X^2+2 X^2+2 X^2+2 X^2+2  2  0  0  0 X^2 X^2 X^2 X^2  2  0 X^2 X^2  2  0  2  2 X^2 X^2  0 X^2  2 X^2+2  2 X^2+2  2 X^2+2 X^2+2 X^2+2  2  2  0 X^2  2 X^2 X^2+2 X^2+2  2 X^2  0  0  0  2  2 X^2 X^2+2 X^2+2
 0  0  0  2  0  0  2  2  2  2  2  0  2  0  0  2  2  2  2  0  0  0  2  0  2  2  0  2  0  0  0  2  0  0  2  2  0  0  2  2  2  0  0  2  2  0  0  2  2  0  2  0  2  2  2  2  0  2  2  0  0  0  0  0  2  0  2  2  2  0  2  2  2  2  0  0  2  2  0  0  0  2  0  2  2  2  0  0  2  2  0  0
 0  0  0  0  2  0  0  0  0  2  2  2  2  2  2  2  2  0  0  2  2  0  0  2  0  2  0  2  0  0  2  2  2  0  0  2  0  0  2  2  0  2  2  0  2  2  0  0  0  2  2  2  0  2  2  2  2  0  0  0  2  0  0  0  2  0  2  2  0  2  0  0  0  2  2  0  2  2  2  2  0  2  0  0  2  0  2  0  2  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+183x^88+96x^90+1488x^92+96x^94+183x^96+1x^184

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 1.39 seconds.