The generator matrix

 1  0  0  1  1  1 X+2  1  2  1  1  X  1  0  1  1  2 X+2  1 X+2  1  2  1  1  0  X  1  1  1  X  0  1  1  1  1 X+2  0  2  1  1  1  1 X+2 X+2  1  2  0 X+2  1 X+2  1  1  1  2  1  0  1  2 X+2  1  2 X+2  1  1  1  1  0  0  1  1  1  1 X+2  2  1  1  1  0  X  1
 0  1  0  0  1 X+3  1  3  1  X  2  X  3  1  2 X+3  0  1 X+1  1 X+2  1  3  2  1  2  X  3 X+1  1 X+2  X  0  0  3  1  1  1  0  1  2  X  X  1 X+1  0  1  2  3  1 X+1 X+2  0  1 X+3  1 X+1  1  0  X  1  1  1 X+2  0  1  1  X  1  0  1  X  1  1  3  3 X+2  0  1  0
 0  0  1  1  1  0  1  X X+1 X+3  X  1 X+3  X X+2  X  1 X+1  1  0 X+1  X X+3 X+1 X+1  1  0  2  2 X+2  1  2  X X+1  2 X+3 X+2 X+1  2  1  3  0  1  3  1  1 X+2  1  2  1 X+2 X+3  0  2 X+3  0  1 X+1  1  2  0 X+2 X+3  3 X+1  3  X  1  1  1  0 X+2 X+1  3  X X+2 X+2  1 X+1  0
 0  0  0  X  0  0  2  0  2  X  0  0  0  0 X+2 X+2  X X+2 X+2 X+2  2 X+2 X+2  2 X+2  X  X  0 X+2 X+2 X+2  X  X X+2  X  0  2  X  2 X+2  0  0  X  X X+2  2 X+2  X X+2  2  2 X+2  X X+2  0  2  X  2  0  X  2  0  2  2  2  X  0  2  0  X  X X+2  X  X  2 X+2  2 X+2  X  0
 0  0  0  0  X X+2 X+2 X+2  X  0  0  2  X X+2  2 X+2  2  X  X  X  0  X X+2  0  X  2  0  0  0  0  X  X X+2 X+2  2  2  0  0 X+2  0 X+2  X  2  0  2  X  2 X+2  X  2 X+2  0 X+2  2  0 X+2  2  2  2  X  2  X  X  X  2  X  X X+2  0  X  X X+2 X+2  X  2  2  0  X  2  2
 0  0  0  0  0  2  0  0  2  2  2  2  2  2  2  0  2  2  2  0  0  2  0  2  0  0  0  2  0  0  2  2  0  2  2  0  2  2  0  2  2  2  0  0  0  2  0  0  2  2  2  0  0  2  0  0  0  2  0  0  0  2  2  2  2  2  0  2  2  0  0  0  2  0  0  2  2  2  0  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+42x^70+170x^71+325x^72+550x^73+706x^74+854x^75+1142x^76+1234x^77+1306x^78+1392x^79+1412x^80+1336x^81+1199x^82+1180x^83+931x^84+764x^85+629x^86+400x^87+304x^88+174x^89+127x^90+84x^91+35x^92+34x^93+19x^94+14x^95+10x^96+4x^97+4x^98+2x^99

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 16.6 seconds.