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

generates a code of length 91 over Z4[X]/(X^2+2) 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 code over GF(2) with n=728, k=12 and d=336.
This code was found by Heurico 1.16 in 1.67 seconds.