The generator matrix

 1  0  0  0  0  1  1  1  2  1  1  1  1 X+2  0  X  1  1  1  1  2  1  1  X  2  X  1  1  2  X  0  1  0  1  1  0  1  X  1  1  X  0  X  1 X+2  1  0  1  X X+2  1  1  X  1  1  X  1 X+2  X  2 X+2  1  1  2  2  1  2  1  0 X+2 X+2  1  0 X+2  0  X  1 X+2  0  1
 0  1  0  0  0  0  0  0  0  2  2  2  2  0  0  0  0  2 X+3  1  1  1 X+3  1  1  1  3 X+1  1  1  X X+2 X+2  1  X  1  3  1  3 X+2  X  1 X+2  X  2  X  1  1  1 X+2  1  1  0 X+2 X+3  1  X X+2  1  1  1 X+2  3  1  1 X+1 X+2 X+1  1  0  2  0  1 X+2  1  1 X+3  1 X+2  2
 0  0  1  0  0  2  1  3  1  X  0 X+1 X+3  1 X+2  1  X  X X+2  X  2 X+1 X+1  3  1  0  1  1  3  X  1 X+1 X+2 X+2  3  0 X+2 X+1  1  2  1 X+3  0  3  0  1 X+1  0  0  1 X+3  2  1  3  3 X+3  2 X+2  3  1 X+3 X+3 X+1 X+1  1  X  X X+3 X+1 X+2  0  0 X+2  X  2 X+1 X+2  X  1  2
 0  0  0  1  0  3  1  2  3  0 X+1  X  3  0  1 X+3  3  X  2 X+2 X+2  0 X+3 X+3  2 X+1  2  1  X  3  1  2  1  1 X+1  3 X+3  1  X X+1  X  2  1  2  0 X+3  X  0  2 X+3 X+2 X+2 X+2  0  X X+3 X+1  1  X  1  0  2 X+2  2  0 X+2  1  1 X+3 X+2  1 X+2 X+2  X X+2  X X+3  3  1  0
 0  0  0  0  1  1  2  3  3 X+1  X  0  3 X+3  1  0  X  2  2 X+3 X+3  X X+1  X  X X+1 X+1 X+2 X+1  X  3  0 X+1  1  1  3  0  1  2 X+1 X+3 X+2 X+1 X+3  1  X  3  2  X  X  X X+1  X  0  1  3  0 X+2  1 X+3  X  3  0 X+1  3 X+3 X+2  2  1  1 X+1  1 X+2  1 X+2  0  1  0 X+3  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+102x^70+428x^71+778x^72+1152x^73+1497x^74+1650x^75+2035x^76+2378x^77+2420x^78+2738x^79+2847x^80+2382x^81+2617x^82+2550x^83+1792x^84+1598x^85+1270x^86+1000x^87+648x^88+354x^89+261x^90+102x^91+89x^92+40x^93+20x^94+10x^95+2x^96+5x^98+2x^99

The gray image is a code over GF(2) with n=320, k=15 and d=140.
This code was found by Heurico 1.13 in 20 seconds.