The generator matrix

 1  0  1  1  1 X+2  1  1  2  1  X  1  1  1  0  0  1  1  1 X+2  1  1  1  X X+2  1  2  1  1  1  0  1  X  1  1  1  0  1  1  1  1  X  1  1  0  1  1  1  1  2  1  1  1  1  1  1  1  1  1  1  1  1  2  1  2  0  X  1  1  1  1 X+2  1  0  X  2  X  1
 0  1  1  0 X+3  1 X+1 X+2  1  2  1  3  X X+1  1  1 X+2  3  0  1  3 X+1  X  1  1 X+3  1  1  X  2  1 X+1  1  2  2  1  1  0 X+3  2 X+3  1  3  2  1 X+3  2  1 X+2  1  1  1  2  1  1 X+3  2  3 X+2 X+1  0  X  1 X+1  X  X  1  X  X  0  0  1 X+1  1  1  1 X+2  0
 0  0  X  0 X+2  0  2  2  X X+2 X+2  2  X  X  X  0 X+2  0 X+2  X X+2  2  0  2  X  X  0  0  2  X  0  X  X X+2  2  0  X X+2  X  0  X X+2 X+2  X  2  2  0 X+2 X+2  2  0  X  0  2  2  0 X+2  X  2  2  X  2  X  0  X  0  2  0  0  2  2  2  X  X X+2  X  X  0
 0  0  0  X  0  0  0  2  2  2  2  0  0  X  X  X X+2 X+2 X+2 X+2 X+2  X X+2 X+2  0  0  X  X  X  0  2 X+2  X  X X+2  0 X+2  X X+2  2  2  2  X  0 X+2 X+2  2  2  0  2  0  2 X+2 X+2 X+2  0  X  0  0  2  X  2 X+2  2  X  X X+2 X+2  X  0  0  X  2 X+2 X+2  0  X  0
 0  0  0  0  2  0  0  0  2  2  0  0  0  2  2  0  2  0  0  2  0  2  0  2  0  2  0  2  2  2  2  0  0  0  2  2  0  2  2  2  0  2  2  0  2  2  2  2  2  0  2  0  0  0  0  2  0  2  2  0  0  2  2  0  0  2  2  0  2  0  2  0  0  0  2  2  0  0
 0  0  0  0  0  2  2  2  0  2  0  0  2  0  0  0  0  0  0  2  2  0  2  2  2  2  2  2  2  0  2  0  0  0  0  0  2  2  2  0  2  2  0  0  0  2  2  0  2  2  2  2  2  2  0  2  2  2  2  2  2  2  2  0  2  0  0  0  2  0  2  2  0  0  0  0  0  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+36x^70+114x^71+224x^72+230x^73+436x^74+252x^75+446x^76+232x^77+392x^78+214x^79+404x^80+174x^81+339x^82+170x^83+176x^84+74x^85+52x^86+36x^87+18x^88+20x^89+17x^90+10x^91+6x^92+6x^93+4x^94+4x^95+5x^96+3x^98+1x^106

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 1.34 seconds.