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

generates a code of length 90 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 86.

Homogenous weight enumerator: w(x)=1x^0+49x^86+100x^87+110x^88+128x^89+235x^90+152x^91+79x^92+128x^93+34x^94+4x^95+1x^96+1x^108+1x^110+1x^130

The gray image is a code over GF(2) with n=720, k=10 and d=344.
This code was found by Heurico 1.16 in 0.86 seconds.