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

generates a code of length 91 over Z4[X]/(X^3+2,2X) who�s minimum homogenous weight is 87.

Homogenous weight enumerator: w(x)=1x^0+168x^87+68x^88+196x^89+200x^90+820x^91+176x^92+188x^93+52x^94+148x^95+10x^96+16x^97+4x^98+1x^176

The gray image is a code over GF(2) with n=728, k=11 and d=348.
This code was found by Heurico 1.16 in 0.984 seconds.