The generator matrix

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

generates a code of length 80 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+218x^70+4x^71+373x^72+40x^73+588x^74+184x^75+708x^76+380x^77+838x^78+420x^79+880x^80+452x^81+842x^82+356x^83+605x^84+132x^85+434x^86+56x^87+295x^88+20x^89+176x^90+4x^91+118x^92+38x^94+27x^96+2x^98+1x^116

The gray image is a code over GF(2) with n=320, k=13 and d=140.
This code was found by Heurico 1.16 in 29.2 seconds.