The generator matrix

 1  0  0  0  1  1  1  X X+2  1  1  1 X+2  0  1  0  2  1  1  0  2  1  1  X  1  1 X+2  0  1  1  1 X+2  1  2  1  1 X+2  1  1  X  1 X+2  1  1  2  0  0  1  X  2  1  1  1  1  0  1  0  1  1  0  0  X X+2  X  1  1  1  1  1  1  1  X  1 X+2  X  0  1  X  1
 0  1  0  0  X  0 X+2 X+2  1  3  3  3  1  1 X+1 X+2  1 X+3  2  1  1  0 X+1  1 X+3  0  X  1 X+1  0 X+3  0 X+2  1  1  3  2  2 X+2  1 X+1  0  2  X  0  1  1  X  1  0 X+3  X X+3  2  1  X  0 X+1 X+3 X+2  1  1  2  1  0  X X+2 X+1 X+3  1  1  1  X X+2  1  1 X+3  2  0
 0  0  1  0  X  1 X+3  1  3 X+2  3  2  0 X+3  1  1  0  0  X  1  X  X X+3 X+3  1 X+3 X+2  0  2 X+1  0  1  1 X+2 X+1  1  1  0  1  3 X+2  X  0  1  1 X+2 X+1  2 X+2  1 X+2 X+3 X+3  0 X+1  0  2 X+1  X  X  3  2  1 X+3 X+2 X+1  0 X+2  2 X+2 X+1  2  0  1  1 X+1 X+3  1  0
 0  0  0  1 X+1  1  X X+3  0  2  0 X+3 X+3 X+1  3  0 X+2 X+2 X+2  0  1 X+3 X+1  3  2  1  1  1 X+3  X  2  X X+1  X X+3 X+2  3  X  2  2  3  1 X+3  0  0 X+3  1  0 X+2  X X+1  2  2 X+3 X+2 X+2  1  3 X+2  1  2  2 X+1  3  3 X+3 X+1  X X+2 X+2  1  1 X+2  3  X  2 X+2 X+1  2
 0  0  0  0  2  0  2  2  2  2  0  0  2  0  2  0  0  2  0  2  2  2  2  0  0  0  0  2  2  0  0  2  2  2  0  2  2  2  2  0  0  2  0  0  2  0  2  0  2  0  0  2  2  0  0  0  2  2  0  2  0  2  2  0  0  2  2  2  0  2  2  0  2  0  0  2  2  0  2
 0  0  0  0  0  2  2  2  2  0  2  0  0  2  2  2  2  2  2  0  2  2  0  0  0  0  2  0  2  0  2  2  2  0  0  2  0  2  0  2  2  2  2  2  0  2  2  0  2  2  0  2  0  0  0  0  0  0  0  0  2  0  2  2  0  0  0  2  0  0  0  2  2  0  0  0  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+99x^70+330x^71+618x^72+742x^73+1107x^74+1002x^75+1306x^76+1260x^77+1347x^78+1152x^79+1286x^80+1254x^81+1213x^82+996x^83+895x^84+496x^85+522x^86+248x^87+225x^88+136x^89+58x^90+46x^91+19x^92+16x^93+4x^94+2x^95+2x^96+2x^98

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 14.8 seconds.