The generator matrix

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

generates a code of length 76 over Z4[X]/(X^2+2,2X) who´s minimum homogenous weight is 68.

Homogenous weight enumerator: w(x)=1x^0+89x^68+294x^69+322x^70+594x^71+573x^72+746x^73+584x^74+792x^75+617x^76+764x^77+545x^78+562x^79+388x^80+446x^81+255x^82+242x^83+132x^84+108x^85+34x^86+44x^87+18x^88+8x^89+16x^90+6x^91+6x^92+2x^93+3x^94+1x^98

The gray image is a code over GF(2) with n=304, k=13 and d=136.
This code was found by Heurico 1.16 in 4.42 seconds.