The generator matrix

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

generates a code of length 93 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 88.

Homogenous weight enumerator: w(x)=1x^0+197x^88+284x^89+528x^90+392x^91+559x^92+344x^93+476x^94+392x^95+428x^96+196x^97+190x^98+48x^99+40x^100+8x^101+4x^102+3x^104+2x^112+2x^114+1x^132+1x^136

The gray image is a code over GF(2) with n=744, k=12 and d=352.
This code was found by Heurico 1.16 in 1.27 seconds.