The generator matrix

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

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+188x^70+36x^71+556x^72+348x^73+854x^74+524x^75+1314x^76+972x^77+1538x^78+1136x^79+1583x^80+1260x^81+1468x^82+944x^83+1238x^84+628x^85+748x^86+236x^87+359x^88+56x^89+210x^90+4x^91+96x^92+38x^94+34x^96+12x^98+3x^104

The gray image is a code over GF(2) with n=320, k=14 and d=140.
This code was found by Heurico 1.16 in 25.3 seconds.