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

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

Homogenous weight enumerator: w(x)=1x^0+127x^88+122x^89+183x^90+468x^91+315x^92+444x^93+137x^94+104x^95+92x^96+10x^97+39x^98+4x^99+1x^100+1x^174

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 1.01 seconds.