The generator matrix

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

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

Homogenous weight enumerator: w(x)=1x^0+219x^72+298x^73+373x^74+474x^75+412x^76+376x^77+399x^78+220x^79+277x^80+210x^81+201x^82+150x^83+146x^84+80x^85+62x^86+60x^87+39x^88+44x^89+40x^90+8x^91+2x^92+5x^94

The gray image is a code over GF(2) with n=312, k=12 and d=144.
This code was found by Heurico 1.11 in 0.512 seconds.