The generator matrix

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

generates a code of length 79 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 73.

Homogenous weight enumerator: w(x)=1x^0+234x^73+312x^74+398x^75+499x^76+328x^77+353x^78+330x^79+293x^80+246x^81+232x^82+232x^83+159x^84+132x^85+113x^86+66x^87+38x^88+44x^89+38x^90+30x^91+8x^93+8x^94+2x^96

The gray image is a code over GF(2) with n=316, k=12 and d=146.
This code was found by Heurico 1.16 in 1.02 seconds.