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

generates a code of length 90 over Z2[X]/(X^4) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+62x^84+102x^86+219x^88+320x^89+674x^90+384x^91+106x^92+64x^93+26x^94+43x^96+30x^98+16x^100+1x^168

The gray image is a linear code over GF(2) with n=720, k=11 and d=336.
This code was found by Heurico 1.16 in 1.01 seconds.