The generator matrix

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

generates a code of length 91 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 84.

Homogenous weight enumerator: w(x)=1x^0+212x^84+1004x^85+1551x^86+2566x^87+2691x^88+3648x^89+3321x^90+3754x^91+3096x^92+3534x^93+2350x^94+2064x^95+1183x^96+882x^97+368x^98+262x^99+144x^100+42x^101+20x^102+26x^103+19x^104+10x^105+13x^106+4x^108+1x^110+2x^112

The gray image is a code over GF(2) with n=728, k=15 and d=336.
This code was found by Heurico 1.16 in 16.3 seconds.