The generator matrix

 1  0  0  1  1  1 X+2  1  X  1  1  1  0  X  0  X  0  1  1  1  1  2  X  1  X  1  1  1 X+2  1 X+2  1  2  1  1  2  1  1 X+2  1  1  X  2  1  1  1  X  1  0  1  0  X  1  1  1  X  1 X+2  2  1  1  1 X+2  1  2  X  1  1  1  0  2  1 X+2  1  1  1  0  1  1  2
 0  1  0  0  1 X+1  1 X+2  0 X+1 X+2  1  1  1 X+2  1  1  3 X+1 X+2 X+2  1  1  2  X  1  0  3  1  1  2  3  1  X X+2  X X+1 X+3  1 X+3  0  1  1  3  0 X+1  1  2  1  3  X  X  2  3  0 X+2  1  2  1  2  0  0  1  3  1  1 X+2 X+3  3  X  1 X+3  0  X  3 X+2  1  2 X+2  1
 0  0  1  1  1  0  1  1  1  3  0  2  1  2  1 X+1 X+2  X X+1  3  2  1  0  X  1  3 X+1  X X+3  0  1  1  X  0 X+2  1  X  3  1 X+2 X+1 X+1 X+1 X+1  1 X+3 X+2  1 X+2 X+1  1  1  X  3  0  1  0  1 X+3 X+2 X+3  2 X+1  1  3 X+1  X  2 X+1  1 X+3  2  1  1  0  1 X+2 X+2  3  0
 0  0  0  X  0  0  2  2  2 X+2  X  X X+2  X  X  0  0  2  0 X+2  X X+2  0  0 X+2  X  2  0  0 X+2  X  2 X+2  2  X X+2  2  0  2 X+2 X+2 X+2  2  2 X+2 X+2  2 X+2  2  2  0  X X+2  0  X  2  2  X  0  X  2  0  0  X  2  X X+2  2  2  2  2  2  X  0  X  X X+2  X  2  X
 0  0  0  0  X  2  X X+2 X+2  2  X X+2  0  X  0  X  2  0  X X+2  2 X+2 X+2  X X+2  X  0 X+2  0  0 X+2  2  0 X+2 X+2  0 X+2  2  2 X+2  X  0  X X+2 X+2  2  0  0 X+2  2  0 X+2  X  0  2  2  X  2 X+2  0  X  2  2  2  2  0  0  0  X  2  0  2  X X+2  2  X X+2 X+2  X  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+88x^72+354x^73+360x^74+512x^75+585x^76+812x^77+604x^78+722x^79+535x^80+754x^81+506x^82+622x^83+403x^84+418x^85+236x^86+246x^87+162x^88+96x^89+78x^90+34x^91+13x^92+26x^93+4x^94+8x^95+2x^96+4x^97+4x^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 4.2 seconds.