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

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+82x^86+16x^87+210x^88+112x^89+224x^90+112x^91+154x^92+16x^93+66x^94+16x^96+12x^98+2x^108+1x^128

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 0.859 seconds.