The generator matrix

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

generates a code of length 93 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 87.

Homogenous weight enumerator: w(x)=1x^0+208x^87+832x^88+1396x^89+1710x^90+1960x^91+1844x^92+1752x^93+1684x^94+1364x^95+1097x^96+840x^97+692x^98+408x^99+185x^100+220x^101+90x^102+40x^103+37x^104+14x^106+4x^107+3x^108+2x^110+1x^112

The gray image is a code over GF(2) with n=744, k=14 and d=348.
This code was found by Heurico 1.16 in 5 seconds.