The generator matrix

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

generates a code of length 79 over Z4[X]/(X^2+2) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+134x^72+742x^73+1515x^74+2344x^75+2484x^76+3972x^77+3209x^78+4614x^79+3424x^80+3582x^81+2347x^82+1892x^83+982x^84+706x^85+348x^86+246x^87+109x^88+60x^89+32x^90+8x^91+10x^93+5x^94+2x^96

The gray image is a code over GF(2) with n=632, k=15 and d=288.
This code was found by Heurico 1.16 in 12.7 seconds.