The generator matrix

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

generates a code of length 78 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+80x^68+452x^69+716x^70+1162x^71+1335x^72+1826x^73+1989x^74+2438x^75+2269x^76+2838x^77+2675x^78+2870x^79+2370x^80+2566x^81+1890x^82+1756x^83+1189x^84+894x^85+504x^86+450x^87+260x^88+120x^89+61x^90+22x^91+14x^92+8x^93+5x^94+6x^95+2x^96

The gray image is a code over GF(2) with n=312, k=15 and d=136.
This code was found by Heurico 1.13 in 19.5 seconds.