The generator matrix

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

generates a code of length 75 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+568x^72+464x^74+592x^76+272x^78+147x^80+2x^96+2x^104

The gray image is a code over GF(2) with n=600, k=11 and d=288.
This code was found by Heurico 1.16 in 114 seconds.