The generator matrix

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

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+163x^72+722x^73+1351x^74+2436x^75+2809x^76+3740x^77+3500x^78+4190x^79+3379x^80+3454x^81+2482x^82+2008x^83+1052x^84+730x^85+370x^86+210x^87+85x^88+20x^89+32x^90+12x^91+7x^92+6x^93+8x^95+1x^98

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 13.6 seconds.