The generator matrix

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

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+125x^72+184x^73+554x^74+460x^75+703x^76+596x^77+696x^78+648x^79+726x^80+588x^81+608x^82+468x^83+524x^84+368x^85+310x^86+176x^87+204x^88+52x^89+92x^90+40x^91+38x^92+4x^93+10x^94+12x^96+2x^98+3x^100

The gray image is a code over GF(2) with n=320, k=13 and d=144.
This code was found by Heurico 1.16 in 4.98 seconds.