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

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

Homogenous weight enumerator: w(x)=1x^0+52x^84+104x^86+16x^87+212x^88+368x^89+568x^90+368x^91+203x^92+16x^93+68x^94+55x^96+8x^98+4x^100+4x^102+1x^172

The gray image is a code over GF(2) with n=720, k=11 and d=336.
This code was found by Heurico 1.16 in 1 seconds.