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  1  1  1  1  1  1  1  1  1  1  1  1 X^2  1  1  1  1  1 X^2  1
 0 X^3+X^2  0 X^2  0  0 X^2 X^3+X^2  0  0 X^2 X^3+X^2 X^3  0 X^2 X^3+X^2 X^3 X^3+X^2 X^3+X^2 X^3 X^3 X^2  0 X^2 X^2  0 X^2 X^3 X^2 X^2 X^3  0 X^3+X^2  0 X^3 X^2 X^2  0 X^2  0 X^3 X^2 X^3  0 X^3+X^2 X^3+X^2 X^3+X^2 X^3 X^3 X^3 X^3+X^2 X^3+X^2 X^2 X^2 X^2  0 X^3 X^3  0 X^3+X^2 X^3+X^2  0 X^3 X^2 X^3+X^2  0 X^3 X^3  0 X^3+X^2 X^3+X^2 X^3+X^2  0 X^3+X^2  0 X^3 X^2 X^3+X^2 X^3+X^2 X^3 X^3 X^3+X^2 X^3+X^2  0  0 X^3+X^2  0 X^3+X^2  0 X^3
 0  0 X^3+X^2 X^2  0 X^3+X^2 X^2  0 X^3+X^2  0 X^2  0 X^2 X^3  0 X^2 X^2 X^3 X^3+X^2  0 X^2 X^2 X^3  0 X^2  0 X^3 X^3+X^2 X^3+X^2  0  0 X^2 X^3 X^3 X^2 X^3 X^2 X^3 X^3+X^2 X^2 X^3  0 X^3 X^2 X^3+X^2 X^3+X^2  0 X^2 X^2 X^3+X^2  0 X^3+X^2 X^3+X^2  0 X^3+X^2 X^3 X^3 X^2 X^3+X^2  0 X^2  0 X^3 X^3  0 X^2  0  0 X^3 X^3 X^3+X^2 X^2  0 X^3 X^3+X^2 X^2 X^2 X^3+X^2 X^3  0 X^3+X^2 X^2 X^3 X^3+X^2  0 X^2 X^3 X^2 X^3+X^2 X^3+X^2
 0  0  0 X^3  0  0 X^3  0  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0 X^3  0  0 X^3 X^3 X^3  0  0 X^3 X^3  0  0 X^3  0 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3  0  0  0 X^3  0 X^3  0  0 X^3  0 X^3  0 X^3  0 X^3  0 X^3  0 X^3  0 X^3  0 X^3 X^3 X^3  0  0  0 X^3 X^3 X^3  0 X^3  0  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3  0  0  0 X^3 X^3
 0  0  0  0 X^3  0 X^3 X^3 X^3 X^3  0 X^3 X^3  0  0 X^3  0  0 X^3  0 X^3  0 X^3 X^3 X^3 X^3  0  0  0 X^3  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3  0  0 X^3  0  0  0 X^3  0  0  0 X^3 X^3  0 X^3 X^3  0 X^3  0  0 X^3  0  0  0 X^3 X^3  0 X^3  0 X^3  0 X^3 X^3  0 X^3  0  0 X^3 X^3 X^3 X^3 X^3  0 X^3 X^3  0 X^3  0
 0  0  0  0  0 X^3  0  0 X^3 X^3 X^3 X^3  0 X^3 X^3 X^3  0  0  0  0  0  0  0  0 X^3 X^3 X^3 X^3 X^3 X^3 X^3 X^3  0  0 X^3  0 X^3  0  0  0 X^3 X^3 X^3  0 X^3 X^3 X^3 X^3 X^3  0 X^3  0  0  0  0  0 X^3 X^3  0 X^3 X^3 X^3  0  0  0 X^3  0 X^3 X^3 X^3 X^3 X^3  0  0 X^3  0  0  0 X^3 X^3  0  0  0  0 X^3  0 X^3 X^3 X^3 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+50x^84+106x^86+165x^88+384x^89+648x^90+384x^91+173x^92+66x^94+57x^96+12x^98+1x^100+1x^176

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 seconds.