The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+150x^72+704x^73+560x^74+708x^75+480x^76+456x^77+308x^78+228x^79+132x^80+140x^81+80x^82+104x^83+8x^84+28x^85+4x^86+3x^88+2x^92

The gray image is a code over GF(2) with n=608, k=12 and d=288.
This code was found by Heurico 1.16 in 0.344 seconds.