The generator matrix

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

generates a code of length 79 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 71.

Homogenous weight enumerator: w(x)=1x^0+116x^71+312x^72+372x^73+513x^74+614x^75+652x^76+712x^77+644x^78+676x^79+715x^80+592x^81+504x^82+496x^83+340x^84+304x^85+241x^86+112x^87+104x^88+68x^89+41x^90+18x^91+17x^92+10x^93+5x^94+2x^96+4x^97+4x^98+1x^100+2x^101

The gray image is a code over GF(2) with n=316, k=13 and d=142.
This code was found by Heurico 1.16 in 4.57 seconds.