The generator matrix

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

generates a code of length 78 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 69.

Homogenous weight enumerator: w(x)=1x^0+172x^69+327x^70+550x^71+775x^72+956x^73+1056x^74+1104x^75+1364x^76+1348x^77+1425x^78+1388x^79+1209x^80+1198x^81+965x^82+748x^83+570x^84+406x^85+310x^86+206x^87+125x^88+70x^89+41x^90+28x^91+14x^92+10x^93+2x^94+8x^95+6x^96+2x^98

The gray image is a code over GF(2) with n=312, k=14 and d=138.
This code was found by Heurico 1.16 in 65.9 seconds.