The generator matrix

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

generates a code of length 76 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 67.

Homogenous weight enumerator: w(x)=1x^0+50x^67+96x^68+152x^69+181x^70+218x^71+260x^72+274x^73+338x^74+352x^75+408x^76+392x^77+307x^78+256x^79+191x^80+148x^81+109x^82+92x^83+72x^84+48x^85+37x^86+44x^87+24x^88+10x^89+17x^90+10x^91+4x^92+2x^94+2x^95+1x^118

The gray image is a code over GF(2) with n=304, k=12 and d=134.
This code was found by Heurico 1.16 in 1.67 seconds.