The generator matrix

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

generates a code of length 80 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+84x^71+370x^72+580x^73+910x^74+784x^75+1221x^76+1180x^77+1352x^78+1324x^79+1302x^80+1244x^81+1298x^82+1064x^83+973x^84+720x^85+690x^86+456x^87+345x^88+168x^89+146x^90+64x^91+68x^92+12x^93+18x^94+6x^96+2x^98+2x^100

The gray image is a code over GF(2) with n=320, k=14 and d=142.
This code was found by Heurico 1.16 in 15.6 seconds.