The generator matrix

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

generates a code of length 78 over Z4[X]/(X^3+2,2X) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+136x^72+788x^73+1017x^74+1772x^75+1811x^76+2244x^77+1828x^78+2010x^79+1354x^80+1356x^81+699x^82+626x^83+311x^84+208x^85+104x^86+60x^87+25x^88+12x^89+6x^90+10x^91+2x^92+2x^94+2x^95

The gray image is a code over GF(2) with n=624, k=14 and d=288.
This code was found by Heurico 1.16 in 3.48 seconds.