The generator matrix

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

generates a code of length 79 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+76x^70+328x^71+610x^72+786x^73+1003x^74+1204x^75+1251x^76+1186x^77+1276x^78+1346x^79+1290x^80+1180x^81+1090x^82+1140x^83+767x^84+556x^85+525x^86+290x^87+193x^88+114x^89+90x^90+40x^91+14x^92+18x^93+3x^94+2x^95+2x^96+1x^98+2x^103

The gray image is a code over GF(2) with n=316, k=14 and d=140.
This code was found by Heurico 1.16 in 15.3 seconds.