The generator matrix

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

generates a code of length 79 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+68x^69+398x^70+808x^71+1080x^72+1472x^73+1880x^74+2032x^75+2286x^76+2528x^77+2550x^78+2692x^79+2824x^80+2460x^81+2216x^82+2108x^83+1613x^84+1328x^85+950x^86+600x^87+373x^88+228x^89+160x^90+44x^91+41x^92+12x^93+6x^94+4x^95+6x^96

The gray image is a code over GF(2) with n=316, k=15 and d=138.
This code was found by Heurico 1.13 in 19.8 seconds.