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

generates a code of length 90 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+86x^84+168x^85+324x^86+254x^87+505x^88+528x^89+618x^90+474x^91+398x^92+204x^93+204x^94+82x^95+93x^96+56x^97+42x^98+22x^99+20x^100+4x^101+12x^102+1x^152

The gray image is a code over GF(2) with n=720, k=12 and d=336.
This code was found by Heurico 1.16 in 1.23 seconds.