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

generates a code of length 91 over Z2[X]/(X^4) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+62x^84+130x^85+163x^86+200x^87+300x^88+432x^89+554x^90+598x^91+503x^92+394x^93+250x^94+172x^95+98x^96+56x^97+60x^98+38x^99+34x^100+8x^101+11x^102+16x^103+9x^104+4x^105+2x^106+1x^148

The gray image is a linear code over GF(2) with n=728, k=12 and d=336.
This code was found by Heurico 1.16 in 1.69 seconds.