The generator matrix

 1  0  1  1  1 X+2  1  1  X  1  1  2 X+2  1 X+2  1  1  1  0  1  1  1  1  2  2 X+2  2  X  0 X+2  2  X  1  1  1  1  1  1  1  1  1  1  2  X  1  1  X  0 X+2  1  1  0  X  0  X  1  1  1  1  1  1  1  1  1  1  1  1  X  1  1  0 X+2  1  X  2  1  1  1
 0  1  1 X+2 X+3  1  2 X+1  1  X  3  1  1  0  1 X+1  0 X+1  1  X  1  X  1  1  1  1  1  1  1  1  1  1  0 X+2  2  X X+1  3  0 X+2  0 X+2  1  1 X+3  1 X+2  1  1  3 X+3  1  1  1  1  X  1  0  1  2  X  X X+1  1  X  1  X  1  1  2  1  1  0 X+2  1 X+3 X+2 X+3
 0  0  X  0 X+2  0  X  2  X X+2  0 X+2  2  2  X  2  X  X  0 X+2 X+2  2  0 X+2  2  0  X  X  0  0  X  X  0  0  X  X  2  2  0  0  X  X  0  2 X+2 X+2 X+2 X+2 X+2 X+2 X+2  X  X  0  2  X  2  2  0  X  0 X+2  2  2  2  0  X X+2  2  0  X  X X+2 X+2  2  0 X+2  X
 0  0  0  2  0  0  0  2  2  0  2  0  0  2  2  0  2  2  2  2  2  0  0  0  2  2  0  2  2  0  2  0  0  0  0  0  2  2  2  2  2  2  0  2  2  2  2  2  0  0  0  2  0  0  2  0  0  2  2  0  0  2  0  0  2  2  0  2  0  0  2  0  0  2  2  0  0  0
 0  0  0  0  2  0  0  0  0  2  2  2  2  2  2  0  2  2  0  0  0  2  2  0  2  2  0  0  0  2  2  2  0  2  2  0  2  0  2  0  0  2  2  2  0  2  0  0  2  0  2  2  0  0  0  2  2  0  0  0  0  2  2  0  2  2  0  0  0  2  0  0  0  2  0  2  2  2
 0  0  0  0  0  2  2  2  0  2  2  0  2  0  0  2  2  0  2  2  0  0  2  0  2  0  2  2  0  0  2  2  2  2  0  0  2  2  2  2  0  0  2  2  2  2  0  0  0  2  2  0  0  2  2  0  0  2  0  0  2  2  2  0  2  0  2  2  2  2  2  2  0  2  0  2  0  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+139x^72+84x^73+304x^74+100x^75+241x^76+84x^77+274x^78+84x^79+211x^80+76x^81+184x^82+60x^83+102x^84+12x^85+26x^86+12x^87+32x^88+12x^90+7x^92+1x^96+1x^100+1x^108

The gray image is a code over GF(2) with n=312, k=11 and d=144.
This code was found by Heurico 1.16 in 0.572 seconds.