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

generates a code of length 76 over Z4[X]/(X^2+2X+2) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+254x^72+64x^73+256x^74+64x^75+768x^76+64x^77+256x^78+64x^79+254x^80+1x^88+1x^104+1x^112

The gray image is a code over GF(2) with n=608, k=11 and d=288.
This code was found by Heurico 1.16 in 0.344 seconds.