The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+37x^86+334x^87+323x^88+322x^89+242x^90+254x^91+146x^92+184x^93+95x^94+68x^95+17x^96+10x^97+1x^98+4x^99+8x^103+1x^124+1x^126

The gray image is a code over GF(2) with n=720, k=11 and d=344.
This code was found by Heurico 1.16 in 0.594 seconds.