The generator matrix

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

generates a code of length 78 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+75x^70+302x^71+397x^72+618x^73+503x^74+794x^75+571x^76+770x^77+589x^78+648x^79+561x^80+560x^81+464x^82+454x^83+212x^84+290x^85+144x^86+118x^87+36x^88+26x^89+10x^90+20x^91+12x^92+8x^93+4x^94+1x^96+3x^98+1x^100

The gray image is a code over GF(2) with n=312, k=13 and d=140.
This code was found by Heurico 1.16 in 4.51 seconds.