The generator matrix

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

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+27x^70+104x^71+246x^72+246x^73+289x^74+380x^75+359x^76+336x^77+327x^78+314x^79+281x^80+340x^81+260x^82+200x^83+145x^84+84x^85+62x^86+18x^87+17x^88+8x^89+17x^90+8x^91+4x^92+8x^93+7x^94+2x^96+2x^97+2x^98+1x^102+1x^112

The gray image is a code over GF(2) with n=312, k=12 and d=140.
This code was found by Heurico 1.16 in 1.24 seconds.