The generator matrix

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

generates a code of length 79 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 70.

Homogenous weight enumerator: w(x)=1x^0+64x^70+156x^71+301x^72+400x^73+441x^74+514x^75+648x^76+680x^77+640x^78+716x^79+649x^80+644x^81+614x^82+478x^83+391x^84+270x^85+176x^86+152x^87+89x^88+42x^89+39x^90+22x^91+24x^92+10x^93+6x^94+8x^95+8x^96+2x^97+2x^98+2x^99+1x^100+2x^102

The gray image is a code over GF(2) with n=316, k=13 and d=140.
This code was found by Heurico 1.16 in 5.61 seconds.