The generator matrix

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

generates a code of length 80 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+98x^71+357x^72+604x^73+752x^74+1006x^75+1177x^76+1212x^77+1318x^78+1328x^79+1282x^80+1172x^81+1055x^82+1224x^83+1100x^84+782x^85+669x^86+446x^87+321x^88+212x^89+133x^90+72x^91+15x^92+18x^93+5x^94+12x^95+3x^96+4x^98+6x^99

The gray image is a code over GF(2) with n=320, k=14 and d=142.
This code was found by Heurico 1.13 in 5.68 seconds.