The generator matrix

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

generates a code of length 93 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 89.

Homogenous weight enumerator: w(x)=1x^0+316x^89+78x^90+80x^91+132x^92+864x^93+92x^94+104x^95+56x^96+292x^97+22x^98+8x^99+2x^120+1x^128

The gray image is a code over GF(2) with n=744, k=11 and d=356.
This code was found by Heurico 1.16 in 0.671 seconds.