The generator matrix

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

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+390x^72+1602x^73+3126x^74+4030x^75+5778x^76+6352x^77+8212x^78+7796x^79+7850x^80+5688x^81+5678x^82+3902x^83+2580x^84+1340x^85+632x^86+320x^87+141x^88+44x^89+36x^90+16x^91+4x^92+8x^93+4x^94+6x^97

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 47.2 seconds.