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  X  X  X  1  1  1  1  1  1  1  1  1  1  1  1  1  1  1 2X+2  1  1  X 2X+2  1 2X+2
 0  2  0  2  0  2  0  2  0  2  0  2  0  2  0  2  0  2  0  2  0  2  0  2  0  2  0  2  0  2  0  2 2X 2X+2 2X 2X+2 2X 2X+2 2X 2X+2 2X 2X+2 2X 2X+2 2X 2X+2 2X 2X+2 2X 2X+2 2X 2X+2 2X 2X+2 2X 2X+2 2X 2X+2 2X 2X+2 2X 2X+2 2X 2X+2  2  2  2 2X+2  0  2  0  2  0 2X  2 2X+2  0  2  0  2  0  2  0  2 2X 2X  0 2X 2X 2X
 0  0 2X  0  0  0 2X  0  0  0  0  0 2X  0 2X  0  0 2X  0 2X  0 2X  0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0  0 2X 2X  0 2X  0 2X  0  0 2X 2X  0 2X  0 2X 2X  0 2X 2X  0 2X
 0  0  0 2X  0  0  0 2X  0  0  0  0  0 2X  0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X  0 2X  0 2X  0 2X  0  0  0  0  0  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0  0  0  0  0  0  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X  0  0 2X 2X 2X  0  0  0 2X 2X  0
 0  0  0  0 2X  0 2X  0  0 2X 2X 2X 2X 2X  0 2X 2X  0 2X  0  0 2X  0 2X  0 2X  0 2X 2X  0 2X  0  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0  0  0 2X 2X 2X 2X 2X 2X 2X 2X  0  0  0  0  0  0 2X 2X  0 2X  0 2X 2X 2X 2X 2X  0  0 2X  0 2X  0 2X 2X 2X  0  0 2X  0  0
 0  0  0  0  0 2X  0 2X 2X 2X 2X  0 2X  0 2X 2X  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0  0  0 2X 2X 2X 2X  0  0  0 2X 2X  0  0  0  0 2X 2X 2X 2X  0 2X 2X  0 2X  0  0 2X 2X 2X 2X  0  0  0 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+68x^86+16x^87+94x^88+176x^89+337x^90+176x^91+78x^92+16x^93+36x^94+17x^96+6x^98+1x^100+1x^106+1x^164

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 1.17 seconds.