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  X  1  1  1  1  1  1  1  X  1  1  1  0  1  X  1 2X  X  1  X  X  2  1  1  1  1 2X  1
 0  X  0 3X+2  2 X+2 2X+2  X 2X X+2  0 X+2 2X+2  X 2X+2 3X X+2 2X  X 2X+2 3X+2 2X 3X+2 2X 3X  2 2X  X X+2 2X+2  0 X+2 2X 3X 2X X+2 3X+2 2X+2 2X+2 3X 3X X+2 2X 2X+2 X+2 3X+2 2X  2  0 2X 3X+2 X+2 3X+2 3X 3X 3X X+2 2X+2  2 3X  2 2X  0  2 2X+2  0  0 2X+2 2X  0 3X+2 2X+2  2 3X+2  X 2X+2 X+2 3X  X X+2 X+2 3X  X  X X+2 2X+2  2 2X 2X  0
 0  0 2X+2  0  2 2X 2X 2X  0  2 2X+2  2 2X+2 2X+2  0 2X+2 2X+2  0  0 2X 2X+2 2X+2  0 2X+2  2  2 2X  2  0 2X 2X+2  0 2X  0  2  2 2X 2X+2  0 2X  0  2  0 2X+2 2X+2 2X+2 2X+2  2 2X 2X  0 2X  0 2X+2 2X+2  2 2X  0 2X+2  2 2X  2 2X  2  0 2X+2 2X  2 2X  2  0  2 2X  0  0 2X+2 2X+2  2  2 2X  0  2  2  0 2X+2  0  0 2X  2  0
 0  0  0 2X+2  0  0  0 2X+2  2 2X+2 2X+2 2X 2X+2  0  2  2 2X+2 2X+2 2X+2 2X 2X  2  0 2X 2X+2 2X 2X  0  2  2 2X+2  0  2  2 2X+2  2  0  2 2X  0  2  2  0  0  0  0 2X  2 2X+2  0  2 2X+2 2X  2 2X+2 2X 2X 2X 2X+2 2X  2 2X 2X 2X 2X+2  0  0  2  2  0  2 2X+2 2X 2X+2  0  2 2X+2 2X+2  0 2X 2X+2  2 2X 2X+2  2 2X+2  0  0  2  0
 0  0  0  0 2X 2X 2X 2X 2X 2X 2X  0  0 2X  0  0 2X 2X 2X 2X  0 2X 2X  0  0 2X  0 2X  0  0  0  0 2X 2X  0 2X  0 2X  0 2X  0  0 2X  0 2X  0 2X 2X  0  0 2X  0  0 2X  0  0 2X 2X 2X 2X 2X  0  0  0 2X 2X 2X  0  0 2X  0 2X  0 2X 2X  0  0 2X 2X  0 2X 2X  0  0  0  0  0 2X 2X  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+221x^84+56x^85+272x^86+216x^87+478x^88+496x^89+720x^90+496x^91+411x^92+216x^93+244x^94+56x^95+107x^96+68x^98+28x^100+4x^102+1x^104+4x^106+1x^160

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 11.9 seconds.