The generator matrix

 1  0  0  1  1  1 2X  1  1  0  1  1  2 X+2  1 3X+2  X  1 X+2  1  1 3X+2  1  X  1  1  1 2X  1  1  1 2X+2  1  1 2X  1 X+2  1  2  1  0 3X+2  1  1  0  1 3X+2 3X+2  1 X+2  1 2X+2  1 X+2  1 2X+2  1  1  1  1  1  1  1  1  1  1  1  1  1 2X+2 2X+2  1  1  1  1  1  X  1  1  1  1  1 3X  1  1  X  0 X+2  1  1  X  1  1
 0  1  0 2X 2X+3  3  1  X 3X 3X 3X+3 X+3  1  1 2X+2  1 3X X+1  1  2 2X+1  1  X 2X 3X 2X+1  2  1 2X+3 X+1  2 2X+2  3 X+3  1 3X  1  1  1 2X+2  1  2 2X+1 3X+2 X+2  X  1  1 X+2 3X 3X+3  1 X+1  1  0 2X 2X 3X+3 X+1 X+2  3 2X  1 2X+3 X+3 X+2 3X+1 3X+2 3X+2  1  1  0 X+2  2  1 X+3  2  3 2X+3 3X 3X+1 2X+1  1 2X+2 3X+1  1  1  0 X+1  0 X+2 3X+2 2X
 0  0  1 3X+1 X+1 2X 3X+1 3X 2X+3  1  3  X X+2 2X+1 3X X+2  1 X+3 X+1 2X+1  X  2  2  1 X+1 2X+2 3X+3  3  1 X+2 2X+3  1 X+2  1 2X+1 3X+3  3 3X+1 X+1 X+2  X  1  0 2X  1 3X+2  X 3X+3  1  1 X+3  2  2 2X 2X+3  1 2X+2  2 X+1  3  X 3X+3  1 X+3 X+2 2X+2  0 X+1  1 X+3 2X+3 3X X+2  0 3X+2  0  1  2 3X 2X  3  3 X+1 3X+1 3X+2  0 X+2  1  X X+2  1 3X+2 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+164x^89+772x^90+676x^91+588x^92+480x^93+360x^94+236x^95+208x^96+172x^97+149x^98+96x^99+113x^100+24x^101+46x^102+8x^103+1x^108+1x^114+1x^120

The gray image is a code over GF(2) with n=744, k=12 and d=356.
This code was found by Heurico 1.16 in 0.578 seconds.