The generator matrix

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

generates a code of length 93 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 90.

Homogenous weight enumerator: w(x)=1x^0+400x^90+256x^91+358x^92+168x^93+340x^94+176x^95+202x^96+40x^97+80x^98+13x^100+4x^102+8x^106+1x^116+1x^144

The gray image is a code over GF(2) with n=744, k=11 and d=360.
This code was found by Heurico 1.16 in 13.6 seconds.