The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+384x^72+1578x^73+2660x^74+4782x^75+5529x^76+7246x^77+6940x^78+8356x^79+7010x^80+6850x^81+4957x^82+4220x^83+2261x^84+1482x^85+666x^86+356x^87+145x^88+60x^89+33x^90+14x^91+6x^92

The gray image is a code over GF(2) with n=632, k=16 and d=288.
This code was found by Heurico 1.16 in 48 seconds.