The generator matrix

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

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+200x^70+256x^71+689x^72+572x^73+1044x^74+1072x^75+1327x^76+1100x^77+1470x^78+1208x^79+1466x^80+1220x^81+1279x^82+860x^83+804x^84+536x^85+502x^86+304x^87+253x^88+24x^89+92x^90+12x^91+59x^92+4x^93+20x^94+7x^96+1x^98+2x^100

The gray image is a code over GF(2) with n=316, k=14 and d=140.
This code was found by Heurico 1.16 in 17.3 seconds.