The generator matrix

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

generates a code of length 80 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 72.

Homogenous weight enumerator: w(x)=1x^0+65x^72+298x^73+413x^74+584x^75+662x^76+710x^77+724x^78+610x^79+710x^80+576x^81+517x^82+454x^83+416x^84+418x^85+282x^86+260x^87+192x^88+106x^89+72x^90+56x^91+32x^92+20x^93+8x^94+2x^95+2x^96+2x^99

The gray image is a code over GF(2) with n=320, k=13 and d=144.
This code was found by Heurico 1.13 in 1.67 seconds.